It's been a long time since I used Ubuntu, but at the time I did I recall running into issues keeping too many old kernels. They were stored in a fixed space folder (or maybe partition?) that was like 100MB and sometimes wouldn't clear out automatically, so I remember this. May not be relevant now, but if it is, space in the storage folder is the limiting factor so you would need to change that. If it IS a partition, then you would need to deal with all that is involved with that.
edited to add that my current OS only stores three or four as well. I have never really dived into it.
Wow, I thought I drank a lot of tea, but it's rarely more than a liter. This is insanity!