Is it possible to make a cancer cell that doesn’t encode any neoantigens?
Immunosurveillance of cancer cells is predicated upon multiple "signals" derived from the cancerous cells and their microenvironment. 

I should point out tumor mutational load (Figure 1). A sort of take-home point here is that certain indications have less mutations and thus less neoantigens than others. You also have to take into consideration the stage of the tumor, though. Stage IV tumors have amassed more mutations than stage I/II.




Figure 1. Mutational prevalence by indication. A higher prevalence predicts a higher neoantigen frequency or mutational load for that cancer histology. (1, 2)

It's interesting to point out the bottom part of figure 1 where the authors of a separate review note for us where it's believed the disconnect between traditional checkpoint blockade immunotherapy and CAR-T immunotherapy exists. Just to educate a bit on the subject, checkpoint blockade targets T cells, the drivers of antigen-dependent cell killing. T cells naturally infiltrate the tumor as it develops and attempt to mount an attack. One of the methods tumors use to evade T cell killing is through persistent antigen, expression of inhibitory receptors and secretion of inhibitory molecules. Checkpoint blockade immunotherapy uses antibodies against the inhibitory receptors such as PD-1 (Opdivo, Keytruda), it's ligand PD-L1, CTLA-4 (Yervoy), Tim3, Lag3, and so forth. This attempts to lift the dampening effect these receptors have on T cells so that they may resume killing. The T-antigen-dependent paradigm is also supported by such publications which look at checkpoint blockade in the setting of clonal T cell diversity and confirm that (1) a diverse repertoire of T cell clones result in successful checkpoint blockade, and (2) enrichment of certain clonotypes within the repertoire, presumably the antigen-specific clonotypes, further indicates a response (3).

So below that are indications circled in red, notably the histologies with a low neoantigen frequency. The idea behind CAR T cells is that I can take advantage of T cell biology, notably that T cells recognize antigen with a receptor and kill the target cell. So just backing up to checkpoint blockade immunotherapy real quick, say a patient has melanoma which can consist of 1000s of mutations and 100s of neoantigens. There is a greater chance that an infiltrated T cell has specificity for any particular antigen. So how about a glioblastoma patient? They may have 10-20 neoantigens, or as you said they may have no neoantigens, at least none that their T cells are specific against. So checkpoint blockade may not be so effective. CAR stands for chimeric antigen receptor. It's essentially a monoclonal antibody against one target connected to a linker connected to the intracellular domain of a T cell receptor. Hematologic malignancies such as NHL like diffuse large B-cell lymphoma are commonly targeted for a B cell receptor known as CD19. So all you have to do is make your CAR CD19 specific and transfect the T cells with it in place of their own T cell receptor or TCR. So the basic process behind CAR is I isolate your T cells as with leukapheresis, lentivirally transfect with my anti-CD19 CAR, expand, and infuse. There are two CD19 CAR T products with great response rates on the market (Kymriah, YESCARTA). The whole reason these are good is because we can direct them to whatever antigen we want (of course be careful about self-antigens, see autoimmunity). 



Figure 2. Schematic of CAR T cell therapy. (4)

The CAR T approach is in fact because the neoantigen load is low or non-existent, which is problematic for un-modified T cells, and thus problematic for standard-of-care treatments like checkpoint blockade.

As such, there are other ways, and other cells that can handle some of the abnormalities presented by tumors as a whole. This includes the presence of danger/damage-associated molecular patterns (DAMPs) and the regulation of surface receptors, for example, NK receptor ligands such as MIC. 

The way DAMPs work is that a milieu of molecules are secreted by cells that are damaged or transformed, signaling cells of the innate immune system. One of the issues is that the DAMPs promote an inflammatory environment. This means that yes, you get immune cells checking out the situation, but that some of these are good immune cells and some are "bad" (myeloid-derived suppressor cells (MDSC), tumor-associated M2 macrophages (TAM), or T-regulatory cells (Treg)). These dampen the immune response both through inhibitory cytokine release like IL-10, and expression of inhibitory receptors like PD-L1.

 

Figure 5. The molecules secreted by the inflammatory tumor microenvironment both help and hurt the immune response. (5).

And then the idea behind NKR ligands is pretty straightforward: Natural killer (NK) cells patrol your body routinely for abnormalities and are licensed to kill cells that are abnormal. For example, all nucleated cells express class I major histocompatibility complex (MHC-I) on their surface. Some receptors like MIC are also present on the cell surface that engage receptors on the NK cells like NKG2D in distress. So what do cancers do? They sometimes express truncated and thus inactive MIC, express no MHC but also express inhibitory receptors to NK cells, and so forth. 

Everything is summed nicely in the following figure on cancer immunoediting (Figure 7). Note that while things are working normally, the immune system can handle the tumor load. As the scales tip, and this could be for example, your T cell response edits out an immunoantigen but doesn't take care of the whole tumor, resulting in growth that those T cells no longer respond to. As this happens, the cancer becomes increasingly invasive.



Figure 7. Cancer immunoediting. (7).

So just to clarify at the end, there probably isn't a case where the immune system isn't responding at all unless you had chemotherapy that destroyed your immune system. Inflammatory environments alone are sufficient for your immune cells to at least check out the tumor. In fact, and I cant find the paper now but I'll try, investigators even found naïve T cells in the tumor microenvironment simply due to the inflammation. We could also get into "hot" and "cold" tumors, but that's out of scope here (take-home point, cold tumors aren't inflamed and are known to contain less immune infiltrate). I used immunotherapy as a vehicle to get my point across, note that this answer isn't about immunotherapy but rather about immune escape and mutational load theory.