Ipilimumab With or Without Dabrafenib, Trametinib, and/or Nivolumab in Treating Patients With Melanoma That Is Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria:

* Study participants must have histologically or cytologically confirmed unresectable or metastatic malignant melanoma
* Study participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam
* Study participants must have completed any prior treatment at least 3 weeks prior to treatment on this protocol; prior treatments may have included chemotherapy however may not have included BRAF or MEK inhibitors or immunotherapies (interleukin-2, ipilimumab, anti-programmed death \[PD\]1 antibodies etc.) excluding vaccine therapy; prior treatment with interferon in the adjuvant setting is allowed, though prior treatment with ipilimumab in the adjuvant setting is not; prior radiation therapy is allowed though must have included no more than 3000 centigray (cGy) to fields including substantial marrow
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Absolute neutrophil count (ANC) \>= 1.2 x 10\^9/L
* Hemoglobin \>= 9 g/dL
* Platelets \>= 100 x 10\^9/L
* Albumin \>= 2.5 g/dL
* Serum bilirubin =\< 1.5 x institutional upper limit of normal (ULN) except subjects with known Gilbert's syndrome
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x institutional ULN
* Serum creatinine =\< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) \>= 50 mL/min
* Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.3 x institutional ULN; subjects receiving anticoagulation treatment may be allowed to participate with INR established within the therapeutic range prior to randomization
* Left ventricular ejection fraction \>= institutional lower limit of normal (LLN) by echocardiogram (ECHO)
* Able to swallow and retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels
* Patients must have BRAFV600E or BRAFV600K mutations, identified by a Food and Drug Administration (FDA)-approved test at a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory (lab); if test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided
* Therapeutic level dosing of warfarin can be used with close monitoring of PT/INR by the site; exposure may be decreased due to enzyme induction when on treatment, thus warfarin dosing may need to be adjusted based upon PT/INR; consequently, when discontinuing dabrafenib, warfarin exposure may be increased and thus close monitoring via PT/INR and warfarin dose adjustments must be made as clinically appropriate; prophylactic low dose warfarin may be given to maintain central catheter patency
* Women of child-bearing potential must agree to use adequate contraception (barrier method of birth control, or abstinence; hormonal contraception is not allowed) for the duration of study participation, and for at least 2 weeks after treatment with dabrafenib or for 6 months after dabrafenib in combination with trametinib; should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately
* All prior treatment-related toxicities must be Common Terminology Criteria for Adverse Events (CTCAE) version (v)4 grade =\< 1 (except alopecia) at the time of randomization
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Prior systemic anti-cancer therapy (chemotherapy with delayed toxicity, extensive radiation therapy, immunotherapy, biologic therapy, or vaccine therapy) within the last 3 weeks; chemotherapy regimens without delayed toxicity within the last 2 weeks preceding the first dose of study treatment
* Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) preceding the first dose of study treatment and during the study
* Study participants with a history of prior treatment with BRAF or MEK inhibitors
* Study participants who had prior treatment with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways
* Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded; these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded; patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible; patients with rheumatoid arthritis and other arthropathies, Sjögren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible

  * Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event)
* Study participants who have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; inhaled or topical steroids and adrenal replacement doses \< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease; patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); physiologic replacement doses of systemic corticosteroids are permitted, even if \< 10 mg/day prednisone equivalents; a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted
* Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation should be evaluated for the potential need for additional treatment before coming on study
* Study participants with known immune impairment who may be unable to respond to anti-cytotoxic T-lymphocyte antigen 4 (CTLA 4) antibody and/or anti-PD-1 antibody
* Study participants with brain metastases are excluded unless these have been definitively treated and are radiographically stable for at least 1 month; the study participant must also demonstrate a stable physical exam and must have discontinued systemic steroids for treatment of edema related to brain metastases or treatment for over 7 days
* Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO)
* Current use of a prohibited medication; patients receiving any medications or substances that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A (CYP3A) or cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8) are ineligible; current use of, or intended ongoing treatment with: herbal remedies (e.g., St. John's wort), or strong inhibitors or inducers of P-glycoprotein (Pgp) or breast cancer resistance protein 1 (Bcrp1) should also be excluded
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
* A history of hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (with the exception of cleared HBV and HCV infection, which will be allowed)
* Patients with history of rat sarcoma (RAS) mutation-positive tumors are not eligible regardless of interval from the current study; Note: prospective RAS testing is not required; however, if the results of previous RAS testing are known, they must be used in assessing eligibility
* History or evidence of cardiovascular risks including any of the following:

  * QT interval corrected for heart rate using the Bazett's formula QTcB \>= 480 msec
  * History of acute coronary syndromes (including myocardial infarction or unstable angina), coronary angioplasty, or stenting within the past 24 weeks prior to randomization
  * History or evidence of current class II, III, or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system
  * Intra-cardiac defibrillators
  * Abnormal cardiac valve morphology (\>= grade 2) documented by ECHO; (subjects with grade 1 abnormalities \[i.e., mild regurgitation/stenosis\] can be entered on study); subjects with moderate valvular thickening should not be entered on study
  * History or evidence of current clinically significant uncontrolled cardiac arrhythmias; clarification: subjects with atrial fibrillation controlled for \> 30 days prior to dosing are eligible
  * Treatment refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mm Hg which cannot be controlled by anti-hypertensive therapy
* Any condition which in the investigator's opinion makes the subject unsuitable for study participation
* History of retinal vein occlusion (RVO)
* History of interstitial lung disease or pneumonitis