Since you want to have a human immunotherapy response in a mouse system that will not have a mouse vs human tumor graft reaction, you should look into the Jax (Jackson Labs, Bar Harbor, ME) collection of humanized NSG mice. They lack a mouse immune system, but have been "humanized" by injection of a human bone marrow (or a subset of those cells) to provide a human immune response (however, the mice have a limited lifespan because of this). Check the Jax website for details about which of their humanized NSG mice might best fit the requirements for the endpoints of your study.

PDX models are in general not suitable for immunotherapy studies, since nude mice or SCID mice do not have a functional immune system. Syngeneic models are in general more suitable for these studies, such as for lung cancer Lewis Lung and M109, while there are other models for other tumors as well

This will depend on the mechanism of action through which your therapeutic attains efficacy.

Setting aside mechanism, you will need an immunodeficient model to enable PDX engraftment, and the model will also need to be engrafted with immune cells to enable the immunotherapy study. Super-immunodeficient models like NOG mice (Taconic) or NSG mice (Jax) tend to be most permissive for PDX and human immune system engraftment.

If your efficacy mechanism relies on T cells, NOG mice engrafted with PBMCs of CD34+ hematopoietic stem cells (HSCs) may be appropriate. However, there are important experimental considerations that would affect choice between the two models.

If your immunotherapy depends on NK cells, you would need to consider a model like hIL15-NOG engrafted with human NK cells. The SRG-15 or hIL2-NOG models engrafted with HSCs could also work, but each of these models also has strengths and weaknesses that should be considered.

Relative to the aforementioned models, NOG-EXL mice and NSG-SGM3 mice will support enhanced myeloid lineage development from engrafted HSCs, making them the best option for immunotherapies that depend on myeloid lineage cells. However, just like the other models listed previously, there are many other considerations that can influence decision of the best model for your study.

If you can provide me more details on the therapeutic, I may be able to provide a better answer and potentially some links to reference efficacy data.