Playing a similar pawn structure with reversed colors for black is a defense known as the semi-Slav:
[FEN ""]
[Title "The semi-Slav"]
1. d4 d5 2. c4 c6 {The Slav defense to the Queen's gambit.} 3. Nf3 Nf6 4. Nc3 e6 {The semi-Slav defense to the Queen's gambit.}
The main characteristic of said structure are the pawns on c6, d5 and e6, mirroring the ones on c3, d4 and e3 that characterize the Colle-like systems. The standard development for black also follows the general guidelines that are common in the Colle, that is, Bd6, 0-0 (although on some variations this move is delayed), Ngd7 and e4 when allowed.