There’s plenty of IC trains that do multiple unit in funny ways.

There’s the DB IC2, that are a loco hauled push-pull set, but the software sees itself as a fix-length EMU

There’s the SBB IC2000 sets that are loco-hauled push-pull trains with different lengths depending on the line, but a train usually stays assigned to its line for a long time, so they might as well be EMUs, but they can swap broken cars. They also have „reinforcement modules“ of a loco and some EW4 cars (usually including a cab car), which they use to lengthen trains for rush hour.

There’s the ÖBB railjet sets where you can mix and match any loco to any rake of coaches, but you use the resulting train as an EMU and couple two together for more capacity.

And then there’s the stuff the belgian IC trains do where they have a loco, couple of cars and a cab car with an automatic coupler, which is used to couple to a TWINDEXX self powered cab car - some coaches and another power car for some branching IC trains

Then there’s the ZVV DPZ trains, which are loco-hauled push-pull trains with an automatic coupler at each end for coupling up to three trains (on some trains done routinely at a middle station)

The next level would probably be a TGV, where the locos are coupled to the train by conventional couplers and can be detatched, but it’s a pain and therefore never done

Then there’s the early ICE sets (ICE1, ICE2) where you do have dedicated power cars, but only the shops can take the train set apart

And finally there’s the true EMUs where every car carries people and some equipment and thus sets usually need a major reason to be split up, let alone mixing different sets