Here are 2 examples of post-modifying a superlative adverb phrase with a clause containing an ellipted modal verb:
I do the best I can with what I have.
I go about my business, make money, help society the best I can and try to promote free trade in this world.
You know, I did the best I could with what I had.
C1 English Grammar Profile point 118 in the category of CLAUSES is defined as:
‘the best’ as a superlative adverb + pronoun + ellipted ‘can’ or ‘could’.
An iWeb search for:
the _RRT _P can|could .
1 THE BEST I CAN. 1455
2 THE BEST THEY CAN. 840
3 THE BEST I COULD. 650
4 THE BEST THEY COULD. 252
5 THE MOST THEY CAN. 19
6 THE MOST I CAN. 18