Sure, that's the problem with cancer. But to get there first, your immune repertoire has become less diverse and developed some holes due to infections, dysbiosis, aging, etc.

There's usually going to be some signal though even if it was just localized downregulation of some proteins on immune cells induced by a cancer to escape detection. The trouble there is that may be swamped in a systemic serum sample. Looking at subsets are more useful to improve signal to noise ratio like looking at extracellular vesicles released by tumour and immune cells for messaging purposes