A Study of IOV-5001 in Adults With Advanced Solid Tumors

Inclusion Criteria: 1. Participant must be ≥ 18 years of age at the time of signing the informed consent. 2. Diagnosis: NSCLC: Participant has a histologically or pathologically confirmed diagnosis of metastatic Stage IV NSCLC (squamous, nonsquamous, adenocarcinoma, large cell, or mixed histologies) without epidermal growth factor receptor (EGFR), anaplastic lymphoma kinase (ALK), or ROS proto-oncogene 1 (ROS1) genomic alterations. TNBC: Participant has a histologically or pathologically confirmed diagnosis of unresectable or Stage IV breast cancer. CRC: Participant has a histologically or pathologically confirmed diagnosis of Stage IV CRC. HNSCC: Participant has a histologically or pathologically confirmed diagnosis of Stage III or IV HNSCC not amenable to curative intent treatment. 3. Radiographic disease progression: Participant has radiographic disease progression after the most recent line of therapy. 4. Disease-specific criterion: NSCLC: Radiographic disease progression occurred: * After having received platinum-based chemotherapy and an immune checkpoint inhibitor, either administered concurrently or sequentially for Stage IV disease. * Within 6 months of completion of the platinum component of platinum-based chemotherapy in the adjuvant or neoadjuvant setting and having progressed after receiving an immune checkpoint inhibitor in the neoadjuvant, adjuvant, or metastatic setting. TNBC: Participant has received up to 3 prior lines of therapy. These must include at least one prior line of cytotoxic chemotherapy for unresectable or Stage IV breast cancer, regardless of ER, PR, or HER2 status at the time it was given. CRC: Participant has received up to 3 prior lines of therapy. These must include a fluoropyrimidine, oxaliplatin, irinotecan, an anti-VEGF therapy, an anti-EGFR therapy (for RAS/rapidly accelerated fibrosarcoma \[RAF\] wild-type disease if the tumor originated in the left side of the colon), and an immune checkpoint inhibitor (for microsatellite instability high \[MSI-H\] or deficient mismatch repair \[dMMR\] disease. HNSCC: Participant has received up to 3 prior lines of therapy. These must include an immune inhibitor and platinum-based chemotherapy unless platinum ineligible due to pre-existing hearing loss, Grade \>= 2 tinnitus, Grade \>= 2 peripheral neuropathy, or allergy to platinum. 5. Disease-specific criterion: NSCLC: Participant has received up to 3 lines of prior therapy. These must include an appropriate health authority-approved targeted therapy for participants who have actionable mutations (other than EGFR, ALK, or ROS1 genomic alterations) if eligible and available. TNBC: Participant has progressed on or is ineligible for other standard of care therapies including, but not limited to: sacituzumab govitecan, poly(ADP-ribose) polymerase (PARP) inhibitors (if breast cancer gene \[BRCA\]1 or BRCA2 mutated), trastuzumab deruxtecan (if HER2low), and pembrolizumab (for PD-L1 combined positive score \[CPS\] \>= 10). CRC: Microsatellite instability and/or mismatch repair mutational status must have been previously determined based on archival tumor biopsies. HNSCC: Participant has documented PD-L1 status. 6. The participant has an ECOG performance status of 0 or 1 and an estimated life expectancy of \> 6 months. 7. Participant is assessed as having at least one resectable lesion (or aggregate lesions) with an estimated minimum diameter of 1.5 cm (short axis) for IOV-5001 generation. Exclusion Criteria: 1. Participants with symptomatic untreated brain metastases. Participants with brain metastases may be enrolled with considerations and discussion with medical monitor. 2. Participant has an active medical illness(es) that, in the opinion of the investigator would pose increased risks for study participation. Participant has evidence of any active viral, bacterial, or fungal infection requiring ongoing systemic treatment or identified during screening. 3. Participant has any form of primary immunodeficiency (eg, severe combined immunodeficiency disease \[SCID\] or AIDS). 4. Participant has a history of hypersensitivity to any component of the study intervention. 5. Participant had another primary malignancy within the previous 3 years (except for those that do not require treatment or have been curatively treated \> 1 year ago, and in the judgment of the investigator does not pose a significant risk of recurrence including, but not limited to: in situ carcinoma of the cervix, early stage skin cancer, including non-melanoma skin cancer, ductal carcinoma in situ (DCIS) or lobular carcinoma in situ (LCIS) of the breast, prostate cancer with Gleason score ≤ 6, or superficial bladder cancer). 6. Participant has a history of allogeneic organ transplant or any form of cell therapy involving prior conditioning chemotherapy within the past 20 years. 7. Participant requires systemic steroid therapy \> 10 mg/day of prednisone or another steroid equivalent dose. Participants receiving steroids as replacement therapy for adrenocortical insufficiency at ≤ 10 mg/day of prednisone or another steroid equivalent dose may be eligible. 8. Participant received or will receive a live or attenuated vaccination within 28 days prior to the start of the NMA-LD preparative regimen. 9. Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study.