What can a familiar aid with?

[NRSASD]

A player of mine has decided to make a dwarven fighter/mage who specializes in one handed weapon use and grappling. He asked me if familiars (from the wizard spell, not the warlock) could use any action beside attacking. I said sure, what did you have in mind? "Using aid another on me when I make grapple checks, so I'll always have advantage"

Well Playground, what's the RAW? Anyone else run into this tactic? How did your table rule on it?
As always, thanks for any and all help!

[Desteplo]

Wizard familiar can’t attack
-but they give help action, so they can provide advantage on your turn. But not their escape attempts.
-dodge
-dash
-they use their reaction to deliver touch spells for the wizard

[Ventruenox]

Not too different from the Rogue using a familiar to always get sneak attack. It's legal, but it also puts the familiar in jeopardy. If the familiar is being used in combat as a tactic, it should be a valid target.

But for the love of your preferred Diety: let's not rehash the invisible familiar and targeting debate again on this thread. This is stated to be a Wizard's familiar.

How does he plan on using the familiar to give the Aid action? You can and probably should challenge him to RP just what the familiar does. Whisper in the opponent's ear? Tickle him? Stick him with a pointy pin? (Last one would constitute an attack). Repetition of the same tactic should also carry with it consequences - there are only so many times hearing "Boo" whispered into one's ear will have an effect if you are wrestling. If it is an Owl with flyby, there can be an archer ally of the one being grappled who notices this pesky bird causing trouble.

Don't look to punish your players for coming up with a viable build/combo, but certainly challenge them to be creative with the implementation.

[JackPhoenix]

Note that familiars are tiny, and thus can't grapple with anything above small size. Unlike attack, using Aid Another for ability checks requires the creature to be able to make the ability check on her own.