"He would have done anything you [would ask/would have asked/had asked] him to"

He would do anything you asked him to.

"Would" is the past tense of "will".

I can't think of the employment of a tense, which conveys your intended meaning. The closest I can get to one is:

"He would have done anything you asked him to."

Though this may not be totally immune to misconstrual, as it may suggest contingency on a condition.

"He would have done anything (if condition were true) you asked him to."

It's true as others have suggested that it's simpler to say:

"He would do anything you asked him to."

But this isn't totally unambiguous, as evidenced by the meaning apparent in:

"I would do anything you asked me to."

This doesn't necessarily refer to the past. "Would" doesn't have to refer to the past, eg.: "I would go but I don't have the money".

And "asked" doesn't necessarily refer to the past either, as evidenced by its meaning in:

"If you asked me to jump off a bridge, I'd tell you to go to hell."

It's possible that the most clear way of conveying your desired meaning is to do what FumbleFingers said in their comment, that is, qualify the sentence with extra information as to a time you're referring to:

"Back then, he would do anything you asked him."
- Courtesy of FumbleFingers.

By specifically including "back then", you make an implication that the statement you make applied earlier, but no longer does. But this is an implication, not a necessity.

“Would” is both modal and auxiliary, so tense/past/present has nothing to do with it - that is handled by the verb coming after “would”. As a modal auxiliary, “would” is marking only conditionality or contingency, not time. Separate those two functions and all the complication disappears. – Roaring Fish

It is the third conditional or the past unreal conditional or past hypothetical conditional.

1. He would have done anything you had asked him to

2. He would have anything had you asked him to (Inverted conditional).

The third conditional has an if clause and a main clause. The if clause describes a situation that didn't really happen in the past. It uses the past perfect (‘had’ + past participle). The main clause refers to the result of the unreal imaginary situation in the past. It uses ‘would have’ + past participle.

https://grammar.ctx.ef.com/conditionals/third-conditional-unreal-past#:~:text=The%20third%20conditional%20has%20an,imaginary%20situation%20in%20the%20past.