IOVA: They already have two pivotal trials and could file BLAs next year. In addition, a number of others, including using PD-1+ TIL and PD-1 knockout 'bulk' TIL.
NTLA: They are in the clinic with an auto TCR-T targeting WT1 (expanding into solids within the next few years). Healthy donor CAR-T's are preclinical, with sequential editing for both. Also, they use CRISPR as a screening tool to identify novel edits that enhance trafficking, infiltration, potency, persistence and overcome exhaustion in a range of immunosuppressive TMEs. In addition, are expanding the 'toolbox' with base editing https://www.globenewswire.com/news-release/2021/03/25/2199184/0/en/Intellia-Therapeutics-Presents-New-Data-
TCRR: Next year a PhII will start in four types, with MPM able to move into a seamless pivotal trial. They have a number of next-gen enhancements, such mbIL-15 and a PD-1 'switch' https://cancerres.aacrjournals.org/content/80/16_Supplement/893
Tmunity Therapeutics: NY-ESO-1 isn't a neoantigen. As for pipeline, it is mostly CAR-T's, with them building a library of constructs to overcome the barriers faced like immunosuppressive TMEs. Also, they are working on allo and CRISPR/Cas9 edited.
With your last paragraph, CRSP should file a BLA in beta thalassaemia and sickle cell disease in the next 12-18 months.