What are all the good opening combos?

One well known very good combo is the Caro-Kann + the Slav:

• The main objective of both of these openings is to develop the light-squared Bishop to f5 before it gets locked inside the Pawn chain.
• They tend to lead to roughly similar Pawn structures.
• On average they both tend to lead to positional, quiet and strategic games.
• And most importantly, if you choose both of these openings, against 1. c4 you can play 1...c6 which can transpose into either a Slav (2. d4) or a Caro-Kann Panov/Pseudo-Panov (2. e4).

I would like to know what are all the other possible combinations of openings which work well together.

I am only interested in combos where both openings are sound.

And if possible also explain why exactly the openings work well together.

The caro-kann and the slav are two totally different openings. They are not similar at all.

Black 1 g6

White 1 g3

What more do you need

1 e4 Nf6 and 1 d4 Nc6 for black. Those tricky knights :p

This is probably your best starting point:

https://en.wikipedia.org/wiki/Pawn_structure

Sicilian Dragon + Modern Benoni. Both have similar structures and are sharp and attacking. They can also be paired with 1.c4 2.g3 as White, it has similar structures but it's not sharp and attacking.

Which Black opening against 1.e4 would work well together with the QGD?

French and QGD

Which Black answer against 1.d4 would work well together with answering 1.e4 with 1...e5 2.Nf3 Nc6 ?

there are two ways to judge opening combos. one is to pair pawn structures in the middle game similarity. that is sound logic.

another way is to pair the opening move tree so the openings can match one another. for example black response to white d4 is to enter nimzo-indian, but white can avoid nimzo and force black into queens indian (KID). so it seems logic for black to pair nimzo indian with KID as a combo to reply to 1.d4 from black perspective. is this correct? ty

KID means King's Indian Defense, it is 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6, it does not pair well with the Nimzo.

The Queen's Indian Defense is abbreviated QID, not KID. The QID is 1.d4 Nf6 2. c4 e6 3.Nf3 b6.

The Nimzo, 1.d4 Nf6 2. c4 e6 3.Nc3 Bb4, can't be played against everything, it must be complemented with another defense. If White plays 3.Nf3 then the Nimzo is no longer an option, instead Black will have to choose between QID (3...b6), Bogo (3...Bb4+), QGD (3...d5) where White will have lost his option to play the Exchange Nge2, Modern Benoni (3...c5) where White will have lost his option to play the FPA and the Taimanov. So when White avoids the Nimzo Black is not forced to play the QID, Black has three other options each roughly as good as the QID option.

But pairing the Nimzo with the QID is actually a bit off-topic, because my thread is about pairing a 1.d4 defense with a 1.e4 defense, not pairing a 1.d4 Nf6 2. c4 e6 3.Nf3 defense with a 1.d4 Nf6 2. c4 e6 3.Nc3 defense.