style - Stative and Dynamic Verbs

There are incongruous parallel constructions, but this is a result of incongruous concepts, not of whether or not one or both are stative:

active + active:

I travel around the world and visit all the well-known beauty spots. :-)

I travel around the world and visit all my neighbours. :-(

active + stative:

I travel around the world and own my own plane. :-)

I travel around the world and own my own hamster. :-(

stative + stative:

I have a diploma in cooking and own my own restaurant. :-)

I have a diploma in cooking and own my own hamster. :-(