Yeah, I think I'm just going to default to QGD territory whenever I can't get a Nimzo that I want.
So you ask about 1.d4 Nf6 2.c4 e6 3.Nf3 d5 4.Nc3, and I'll just play 4...Bb4
When I played the QGD I got tired of the position after 4...Be7 5.Bf4 so the vienna / ragozin thing will be something fresh.
It's a bit of a chess.com thing, the obsession with playing c6 and semi-slav, probably based on too much reliance on database stats. In the move order of your example, you could have just played Be7, and developed with castling, b6, Bb7, then c5, or 4...c5 immediately. So you can just play a straightforward Queens Gambit Declined with much less theory to worry about.
The move order I show is very deliberate. I have other things I play in other situations. So I am avoiding all the Bg5 semi-slav stuff. I was thinking I would just have to worry about the meran and anti-meran.
The move order you show cannot be forced. What about 1.d4 Nf6 2.c4 e6 3.Nf3 d5 4.Nc3!
NOW:
If you go Semi-Slav, you have to allow 5.Bg5
If you play 4...Bb4, you are no longer in a Semi-Slav or a Nimzo-Indian, but rather, a Ragozin, which is a line of the QGD (Not sure if it's D37, D38, or D39, or some combination of that).
You can reach it via the Nimzo with 4.Nf3 d5, but most don't transpose to the Ragozin after 4.Nf3 and prefer 4...b6 or 4...c5 with 4...O-O a distant third before 4...d5.