I am a accumulator as well. I do not have the wallet to be a full blown collector of any genre of knife, sword or other bladed tool.
However, I have acquired a good number of bladed tools in the utility category, self defense/emergency rescue, "survival" and bushcraft types. In all categories I have way more than I actually need, and may accumulate a few more based on budget and whim.
There is one category - or perhaps more accurately two - I am starting to accumulate in ernest because they interest me from a historical perspective as well as the practical bladed tool perspective. They are 1930s/World War Two through the Vietnam War military knives and bayonets. So while I don't have the wallet to be a true collector of both, I am hoping to accumulate some of the more common and yes to me, appealing examples.