Testing the Combination of Two Immunotherapy Drugs (Magrolimab and Dinutuximab) in Patients With Relapsed or Refractory Neuroblastoma or Relapsed Osteosarcoma

Inclusion Criteria:

* Patients must have a history of histologically or cytologically confirmed NBL or osteosarcoma
* Patients must have:

  * Relapsed/refractory high-risk neuroblastoma (NBL) (defined as disease recurrence after completion of therapy, progressive disease on therapy, or refractory disease during induction therapy) or
  * Relapsed osteosarcoma (relapsed after frontline therapy and/or there must not be any potentially curative treatment options available at the time of enrollment)
* Cohort B1: Confirmed neuroblastoma: measurable NBL/ganglioneuroblastoma (defined as those lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm with cross sectional imaging (CT scan or MRI), or \>= 10 mm with calipers by clinical exam). Chest x-ray cannot be used to determine eligibility. Lesions must be iobenguane (MIBG) positive, positron emission tomography (PET) avid (if patient has a history MIBG negative disease) or biopsy proven NBL/ganglioneuroblastoma
* Cohort B2: Evaluable NBL (MIBG and/or bone marrow disease only)
* Cohort B3: Measurable osteosarcoma (defined as those lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm (\>= 1 cm) with cross sectional imaging (CT scan, MRI, or calipers by clinical exam). Chest x-ray cannot be used to determine eligibility
* Cohort B4: Patients with relapsed resectable pulmonary osteosarcoma who are scheduled for a surgical resection
* Note: Subjects will not have measurable disease due to recently resected pulmonary metastases. Investigational therapy must begin within three weeks of resection. Staged resections are permissible; investigational therapy will be administered in between resections. Patients should receive one cycle of investigational therapy in between resections but can receive additional cycles to accommodate the most appropriate surgical schedule as determined by the treating physicians. Every effort will be made to have at least half of this cohort (five of ten patients) be those requiring a staged resection
* There is no limit to the number of prior treatment regimens. Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to initiation of study treatment. Acute toxicity of any previous therapy must have resolved to grade 1 or less or stabilized, unless specified elsewhere

  * Myelosuppressive chemotherapy: Patients must not have received myelosuppressive chemotherapy within 3 weeks of initiation of study treatment (6 weeks if prior nitrosourea)
  * Hematopoietic growth factors: At least 7 days must have elapsed since the completion of therapy with a growth factor. At least 14 days must have elapsed after receiving pegfilgrastim
  * At least 7 days must have elapsed since the completion of therapy with a biologic agent, targeted agent, tyrosine kinase inhibitor or a metronomic non-myelosuppressive regimen
  * At least 4 weeks must have elapsed since prior therapy with 131I-MIBG
  * Monoclonal antibodies: At least 3 weeks must have elapsed since prior therapy that included a monoclonal antibody. Patients who have received prior therapy with GD2 antibodies, regardless of response to therapy, will be eligible
  * At least 7 days must have elapsed since the last pharmacologic dose of systemic corticosteroids
* Arm A: Age \>= 2 or \< 18 years of age
* Arm B: Age \>= 2 or =\< 35 years of age
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2; Subjects \> 16 years of age: Karnofsky \>= 50%; Subjects =\< 16 years of age: Lansky scale \>= 50%
* Absolute neutrophil count \>= 1,000/mcL
* Hemoglobin \>= 9.5 g/dL, transfusion support acceptable
* Platelets \>= 100,000/mcL, independent of transfusions
* Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN) for age (sum of conjugated and unconjugated)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x institutional ULN
* Creatinine =\< institutional ULN OR glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* Female patients of childbearing potential must not be nursing or planning to be pregnant and must have a negative urine or serum pregnancy test within 30 days before enrollment and within 72 hours before the first administration of study treatment

  * Note: Females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential
* The effects of Hu5F9-G4 (magrolimab) monoclonal antibody on the developing human fetus are unknown and dinutuximab is known to be teratogenic. For this reason, female patients of childbearing potential must be willing to use one highly effective method of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, during the study and continue for 4 months after the last dose of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately

  * Male patients who are sexually active with a woman of childbearing potential (WOCBP) and who have not had vasectomies must be willing to use a barrier method of contraception (condom plus spermicidal gel) and refrain from sperm donation during the study and for 4 months after the last dose of study treatment. If the partner is pregnant, male patients must use barrier method contraception (condom) during the study and for 4 months after the last dose of study treatment to prevent fetal exposure to study treatment
* All patients and/or their parents or legally authorized representatives must have the ability to understand and the willingness to sign a written informed consent. Assent, where appropriate, will be obtained according to local institutional policy
* Cardiac ejection fraction \>= 45% or shortening fraction \>= 28%, no evidence of physiologically significant pericardial effusion as determined by an echocardiogram (ECHO), multigated acquisition scan (MUGA) or cardiac MRI. No clinically significant electrocardiogram (ECG) findings that in the judgment of the treating investigator would present a contraindication for treatment

Exclusion Criteria:

* History of allergic reactions attributed to compounds of similar chemical or biologic composition to anti-GD2 monoclonal antibody (dinutuximab) or Hu5F9-G4 (magrolimab) monoclonal antibody or other agents used in this study
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Patients who are receiving any other investigational agents
* Pregnant women are excluded from this study because Hu5F9-G4 (magrolimab) is a monoclonal antibody on the developing human fetus are unknown and dinutuximab may cause fetal harm. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Hu5F9-G4 (magrolimab) or dinutuximab, breastfeeding should be discontinued if the mother is treated with Hu5F9-G4 (magrolimab) or dinutuximab
* Patients who have received prior treatment with CD47 or SIRPalpha-targeting agents
* Patients with red blood cell (RBC) transfusion dependence, defined as requiring more than 2 units of RBCs transfused during the 4-week period prior to screening. RBC transfusions are permitted during the screening period and prior to enrollment
* Patients with known inherited or acquired bleeding disorders are not eligible
* Patients with prior hemolytic anemia or Evans syndrome in the last 3 months
* Patients with significant medical diseases that would worsen the risk-benefit ratio of participating in this study. This includes but is not limited to acute myocardial infarction within the last 6 months, unstable angina, significant acute or chronic infections, or severely immunocompromised state
* Patients on the following medications at the time of study treatment initiation:

  * Immunotherapy or immunosuppressive drugs (e.g. chemotherapy or systemic corticosteroids) EXCEPT for the following:

    * The only exception is for patients known to require 2 mg/kg or less of hydrocortisone (or an equivalent dose of an alternative corticosteroid) as premedication for blood product administration in order to avoid allergic transfusion reactions. The use of conventional doses of inhaled steroids for the treatment of asthma is permitted, as is the use of physiologic doses of steroids for patients with known adrenal insufficiency
  * Growth factors (granulocyte colony stimulating factor or granulocyte macrophage colony stimulating factor) EXCEPT for erythropoietin and darbepoietin alpha
  * Herbal remedies with immunostimulating properties (e.g., mistletoe extract) or known to potentially interfere with major organ function (e.g. hypericin)
* Patients administered a live vaccine within 28 days prior to initiation of study treatment
* Patients with active or previously treated central nervous system (CNS) metastasis