This phase II trial tests how well epcoritamab in combination with standard of care (SOC) platinum-based chemotherapy (rituximab, ifosfamide, carboplatin, etoposide \[RICE\], rituximab, cytarabine, dexamethasone, oxaliplatin or carboplatin RDHAP/X\] or gemcitabine and oxaliplatin \[Gem/Ox\]) and autologous hematopoietic cell transplant (HCT) works in treating patients with large B-cell lymphoma (LBCL) that has come back after a period of improvement (relapsed) or that has not responded to previous treatment (refractory). Epcoritamab, a type of bispecific T-cell engager, binds to a protein called CD3, which is found on T cells (a type of white blood cell). It also binds to a protein called CD20, which is found on B cells (another type of white blood cell) and some lymphoma cells. This may help the immune system kill cancer cells. Carboplatin is in a class of medications known as platinum-containing compounds. It works in a way similar to the anticancer drug cisplatin, but may be better tolerated than cisplatin. Carboplatin works by killing, stopping or slowing the growth of cancer cells. Oxaliplatin is in a class of medications called platinum-containing antineoplastic agents. It damages the cell's deoxyribonucleic acid (DNA) and may kill cancer cells. Rituximab is a monoclonal antibody. It binds to a protein called CD20, which is found on B cells and some types of cancer cells. This may help the immune system kill cancer cells. Chemotherapy drugs, such as ifosfamide, etoposide phosphate, cytarabine, and gemcitabine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Dexamethasone is in a class of medications called corticosteroids. It is used to reduce inflammation and lower the body's immune response to help lessen the side effects of chemotherapy drugs. An autologous HCT is a procedure in which blood-forming stem cells (cells from which all blood cells develop) are removed, stored, and later given back to the same person. Giving epcoritamab in combination with SOC platinum-based chemotherapy, such as RICE, RDHAP/X and Gem/Ox, and autologous HCT may kill more cancer cells in patients with relapsed or refractory LBCL.