I hesitate to make a suggestion, but would it make sense to go down the road of a director of football (a proper one, as opposed to the pretend variety some clubs have) and a head coach?
I don't know nearly enough about how things have gone but on the face of it your last three managers (Koeman, Allardyce and Silva) have probably had different footballing philosophies, with the danger that you have a squad upheaval every time there is a change.
We poached Stuart Webber from Huddersfield Town and he sets the philosophy to be followed, and his job is to choose a suitable head coach. Between them they deal with transfers, as opposed to it being a manager who decides unilaterally, with the idea that there will be continuity even if the head coach leaves. We haven't seen this aspect in operation yet, as his first choice, Farke, is still in place, but that is the theory.