One of the things conlangers come up with every now and then - and which really do exist, even - are the verbal equivalents of pronouns.
I am not sure whether there is any "formal" definition of such a pro-verb that is very specific - I figure linguists recognize them when they see them, and I doubt there's much actual formal need, usually at least - to study these as a category of verbs.
I imagine it might be common in languages to have different types of "do" - maybe distinguished by a variety of factors: aspect, transitivity, expected type of result. Like pronouns, I find it likely that pro-verbs would not be "entirely normal" verbs - but rather of the kind that can be auxiliaries (much like pronouns can be determiners) and may be defective (like pronouns may) or have richer systems of inflection (like pronouns may). However, "do" altered along those dimensions is not the only possible pro-verb.
An obvious type of pronoun to look into is the demonstrative pronoun. "What you this.verb" - what is this that you are doing?, "you this.verb any result" - 'does doing this have any result'. Demonstrative adverbs ('thus', 'like this') could of course also reasonably be verbal: thus.verb.imperative: do thus!, [like this].verb.interrog: like this?, 'you thus.verb.interrog? I always this.verb!" - "do you do like that? I do it this way."
Another obvious one is the interrogative verb - essentially "what are you doing", though one could also imagine that "how" could be an auxiliary - in which case a nice system with the demonstratives of manner emerges.
One could of course go further and go for the indefinite pronouns: nothing, something, anything. Here, I recommend reading the post on the typology of indefinite pronouns! "What.verb.2sg?" "Nothing.verb.1sg". "Just anything.verb.imp!", "They something.verb.past.3sg".
Other indefinite pronouns and determiners - like 'other', 'whatever', 'this, that and the other', 'either', 'none', 'neither', could easily lend themselves to verbs.
For a further twist, how about relative verbs? One could of course use them as markers of subclauses in general - an auxiliary that always occurs in a relative subclause - but one could also imagine them as a way of introducing relative subclause-like information about a verb.
I tired am which.verb.1sg always in the evenings
There's of course tons of ways in which these could be extended with normal verbal affixes, imagine
she always knew what I was about to do
"he always re-theirs.verb.participle"
he always redoes what they do