I have been playing Nimzo Indian + Bogo Indian combo since 2010 and this is my favorite opening with both sides. The Nimzo Indian is also a very forgiving opening, one mover order mistake in the opening generally does not leed more trouble than a slightly worse position. The traditonal Nimzo Indian partner is the Queens Indian defence. I do not know why but most white players prefere to play against Queens Indian rather than Nimzo Indian or dodge both by playing 3 g3. The advantage of Bogo Indian is that it works vs both 3 Nf3 and vs 3 g3.
However d-pawn specials are more common to meet than both Nimzo Indian and Bogo Indian together. Due to that I play lines with black that cuts down the workload while still being active and solid.
While I have not played or posted any new moves, in 2012 I asked GM John Emms to make an update on Nimzo 4 Qc2 Nc6 variation at Chesspublishing.com subscription section and so he did and thanked me for my thoughts and a timely reminder and that monts sections update only covered that variation! The update in turn inspired the later book "Opening Repertoire: Nimzo and Bogo Indian" by Christof Sielecki. I have also made som experiments in Nimzo 4 Qc2 Nc6 5 Nf3 that I castle at once instead of playing the book move 5 .. d6. I am also one of few players who regulary plays 4 .. Nc6 vs 4 Nf3 Nimzo where white has nothing better than 5 Qc2 transposing to 4 Qc2 Nc6 Nimzo.
In Correspondence Chess I have played Bogo Indian in several games but no one has allowed Nimzo Indian yet.
The reason for that are that Nimo Indian Defence has a excellent reputation and are as good shape in all line and black has multiple playable setups against each move. I have played more Bogo Indian games than Nimzo Indian games even in over the board chess, but in over the board games I have at least played Nimzo Indian in a few games.
Bogo Indian are on the other hand an underrated opening and thus many white player allows it both over the board and in Correspondence Chess. I have played Bogo Indian in several Correspondence Chess games and never lost a single Bogo Indian game and even won a few games with the Bogo Indian.
For a long time I have been playing with the idea to play the "Nimzo Indian / Queens gambit declined" hybrid called Ragozin. I am currently testing it online before deciding to switch to it or not or to play it as main weapon or as tag team partner to Nimzo. It can transpose into several variations of Nimzo even as independent option an not only as tag Nimzo team partner.