Obviously, one can have a verb that compares things with things. This is the basic notion behind exceed-comparatives and the like, but also verbs like Swedish 'likna' ('to be similar to'). One could also do a simple thing like incorporate verb morphology like tenses and person marking onto a particle, so that 'than him' comes out as a third person verb, "thans". In a language with a more full person morphology, this obviously permits some succinctness, and one could of course also have tense morphology agreeing with the main verb - or even disagreeing to convey ideas like
she is faster than I was
she is fast(er) (and?/but?/that?) than-past-1sg
However, stopping there seems a tad underwhelming. Why not go and do things with voice.
she teaches good/better than-past-pass-1sg
she teaches better than I was taught
Now we can also consider making adverbial participles out of this:
he operates heavier machinery than-1sg-active-ptcpl-advbl
he operates heavier machinery than I
In this case, the point would be to de-emphasize the role of the comparison. Finite 'than' would make the comparison central to the utterance, infinite 'than' would make it peripheral. Maybe peripheral comparison should not (mandatorily?) trigger comparative marking on the adjective.
A thing like this could also permit for a nice way to group together things that are being compared, especially if the verbs of the language have a very rich congruence morphology.
Another turn could be letting this verb take a finite clause as its complement, so a bit analogous to verbs like 'say [that]', this could form a structure along the line of 'than [that]'.
Some less well-baked ideas on top of this then: in an ergative language with this construction, one could permit for intransitive verbal comparison to use either ergative or absolutive nouns for the subject of this particular verb in order to differentiate something, maybe degree of difference or such - absolutive possibly indicating that the subject is considerably less X than the standard of comparison.