**Unfortunately, no, not conventionally.  There is always Wish.**

However, this has been done in previous editions.  So there is precedent out there.

If you were to go this route, you would need to check with your DM, of course.  So I mention previous editions because it is a great source for ideas on how to do this.  In the past this was done through:

- Spells
- Feats
- Rituals (Before rituals were spells)
- Magic Items 
- At a higher level you could often get a more powerful familiar (imp, pseudodragon, etc.)

I will research my old docs to see if I can source these methods, but it might take some time.  If / When I find them, I'll post them here.

Here is one of my favorite articles on improving familiars from [Dragon #181][1] pg 22.  While it is for 2nd Ed, it is easily translatable to 5th, and it seems like a very reasonable place to start when building familiar improvements.


  [1]: https://annarchive.com/files/Drmg181.pdf