Patients must be positive for at least one of the following human leukocyte antigens (HLA): a. HLA-A*02:01, b. HLA-A*02:06, c. HLA-A*24:02 Subject is HLA-A*02:01, HLA-A*02:05, and/or HLA-A*02:06 positive as determined by a central laboratory. (This determination will be made under a pre enrollment screening informed consent form [ICF]. There are no restrictions on the timing of HLA typing for screening and data can be taken from subjects' records). The patient must test positive for HLA-A2 (tested by a CLIA approved laboratory; only the\r\n HLA A*02:01 subtype is eligible) Subject is HLA-A*02:01 and/or HLA-A*02:06 positive. Subject is HLA-A*02:05 in either allele, HLA-B*15:01 and/or HLA-B*46:01 positive. Subject has any A*02 null allele (designated with an \N\, e.g. A*02:32N) as the sole HLA-A*02 allele. Patients must be positive for HLA-A2 based on flow­cytometry or genotyping HLA-A*0201 (HLA-A2.1) positivity by molecular subtyping Patients must express HLA-A*0201 HLA-A*0201 (HLA-A2.1) positivity by molecular subtyping Patients must have the HLA-A*02:01 allele Patients must be HLA-A*1101 positive Subject is HLA-A*02:05 positive in either allele; Subject has HLA-A*02:07 as the sole HLA-A*02 allele (e.g., a subject with HLA alleles A*02:04 and A*02:07 is eligible); or Subject has any A*02 null allele (designated with an \N\, e.g., A*02:32N) as the sole HLA-A*02 allele Subject is HLA-A*02:01 or HLA-A*02:06 positive. Subject is HLA-A*02:05, HLA-B*15:01 and/or HLA-B*46:01 positive. Must be HLA- A*02:01 positive; (retesting is not required for patients who have previous documented HLA- A*02:01 positivity) HLA phenotype positive. Patients must be HLA-A*0201 positive HLA-A*02:01 expression Lack of HLA-A*02:01 expression Patient Human Leukocyte Antigen (HLA) typing should demonstrate HLA-A*01, and/or HLA-A*02, and/or HLA-A*24 restriction. Patients with HLA-A alleles not belonging to any of the following subtypes: HLA-A*01, or HLA-A*02, or HLA-A*24. Subjects must express HLA-A2 phenotype as assessed serologically. HLA-A2 negative patients All study participants must have one of the HLA alleles: HLA-A*02, HLA-A*03, HLAA*11, or HLA-A*24 Patients must be HLA-A*01 positive Patients must express HLA-A*0201 HLA-A*0201 positive by Central Assay Be HLA-A*02+ as determined by Central Laboratory; Patient Human Leucocyte Antigen (HLA) typing should demonstrate HLA-A*01, and/or HLA-A*02, and/or HLA-A*24 restriction. Patients without HLA-A1, or HLA-A*02, or HLA-A*24 restriction. Subjects must be HLA-A2 positive HLA phenotype positive. Note: Patients who were previously HLA-typed for participation in other Immatics' sponsored clinical trials and were HLA phenotype positive may enter IMA202-101 main screening Expression of HLA-A*0201. Expression of HLA-A*0201. Be HLA-A2 positive Subjects must be HLA-A2 positive by central lab Patient is HLA-A2+ HLA-A*0201 positive as determined by deoxyribonucleic acid (DNA) allele-specific polymerase chain reaction (PCR) assay; HLA restriction is not required for cohorts 4 and 5 HLA-A*0201 positive as determined by deoxyribonucleic acid (DNA) allele-specific polymerase chain reaction (PCR) assay\r\n* For cohort 5 after amendment 9 and cohort 6, there is no HLA restriction Subject must be HLA-A*02:01, HLA-A*02:05 and/or HLA-A*02:06 positive. Human leukocyte antigen (HLA)-A*0201 (HLA-A2.1) positivity by molecular subtyping\r\n* Patients with HLA-A*0205 (HLA-A2.5) positivity by molecular subtyping may be eligible if there is demonstration that they can correctly present the MART-1 26-35 epitope as stimulators for interferon (IFN)-gamma production by MART-1 F5 TCR transgenic cells Human leukocyte antigen (HLA)-A*02, HLA-A*03, HLA-A*11 or HLA-A*24 positive patients Must be HLA A*0201, HLA-A*0205, and/or HLA-A*0206 positive by high resolution testing. The patient must express HLA class I allele HLA-A*0201 for NY-ESO-1/LAGE. Blood HLA-A2 phenotype HLA-A02*:01 positive Patient must be HLA-A*0201+ and/or HLA-A*0206+ Subject must be HLA A*02:01, HLA A*02:05 and/or HLA-A*02:06 positive. HLA A*0201 high resolution, 4-digit type is required at HLA-A2 to ensure A*0201 status HLA-A2+ or HLA-A3+ or HLA-A24+ or HLA-A26+ HLA-A*02:01, HLA-A*02:05, and/or HLA-A*02:06 by high resolution testing at a local or central laboratory Patients must be HLA-A2 positive HLA-A2 negative patients HLA-A2 or HLA-A3 haplotype HLA-DPB1*04:01 positive Positive for HLA-A*02:01or HLA-A*02:642 allele. Positive for any of the HLA-A*02 allele other than HLA-A*02:01 or HLA-A*02:642 or the following alleles: HLA-A*02:02, HLA-C*04:04 or HLA-B*51:03.