What is it about the TubeScreamer that makes it uniquely unprofileable, Christoph? This would be good to know, as more overdrive pedals are TS variants than not.
The TS and its clones more work like a distortng compressor rather than a classic distortion.
And no, only a minority of overdrive pedals work like a TS. E.g. some of the old Boss distortions.
Fuzz, Rat and many more are different.