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 many games but only played Nimzo Indian in one single game yet except some of my Ragozin games since the positon can arrise via Nimzo 4 Nf3 d5 move order. I also played a game that started as Bogo Indian, became Nimzo Indian and ended up as Queens Indian.
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. As a bonus, Bogo Indian can also be played vs Catalan (3 g3).
I have played Bogo Indian in many Correspondence Chess games and have only lost two Bogo Indian games. I have also won a few games Correspondence Chess games with the Bogo Indian and have more wins than loses and most of my Bogo Indian games was easy draws, including vs hiegher rated.
In the first game I lost I had analysed a seqvens of moves in the late middlegame to completly equal but managed to commit the last move instead of the starting move and the move was a a concrete postional blunder where the evalution changed from + 0.10 to + 1.4 after whites correct next move and I was slowly crushed. In the other game I lost I dropped the Knight the wrong square in the opening by accident vs a 400 elo higher rated player. It did not lose material and I thougt it transpose to a harmless main like but my opponent found a better move where he got a slight plus and he started to played better Chess than I did on every move so I resigned since I had no counterplay and was competly tied up over the entire board.
For a long time I have been playing with the idea to play the "Nimzo Indian / Queens gambit declined" hybrid called Ragozin Defence. I tested it in 5 Correspondence Chess games before deciding to switch to it or not or to play it as main weapon or as tag team partner to Nimzo. I won the 1st game I played it. Every other of my test games became draws. The defence can transpose into several variations of Nimzo Indian even as independent option and not only as tag team Nimzo team partner. I play Ragozin as main defence using a Queen Gambit mover order in over the board games.