Is immunotherapy possible for tumours which do not have Tumour Specific Antigens (TSA)? If so, doesn't targeting those tumour cells also target other healthy cells, thus causing autoimmunity ?
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.
Monoclonal antibodies can have a range of uses: Avastin (Bevacizumab) directly targets VEGF to inhibit angiogenesis (with obvious side effects). Some mAbs are chemolabeled with a cytotoxic drug that can be delivered to tumor based on normal antigens, but the obvious downside is healthy tissue expression.
There's a fair overview of immunotherapies available here.