Immunotherapy for tumours which do not have TSA
Yes, in some circumstances. 

In some cases the antigen being targeted, even if it leads to loss of normal cells, can be targeted. This is most evident in the targeting of CD19 to treat various forms of B-cell derived tumours. Example of such an application and response biomarkers are described here 
https://www.ncbi.nlm.nih.gov/pubmed/28291388

Secondly, opportunities may be created by the generation of epigenetic states. Cancer-germline antigens are usually only expressed in gonad tissues (which enjoy immune privilege) but are often aberrantly reactivated in tumours, but not in other somatic tissues. This too can create specificity to immunotherapy even if the antigen is not truly tumour-specific, and is rather striking as a phenomenon in testicular cancer.

https://www.ncbi.nlm.nih.gov/pubmed/28555838