user3237: 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.
Enumerate as many combos as you can. But I am only interested in combos where both openings are sound.
And if possible also explain why exactly the openings work well together.

user4362: I don't think there is a single other opening combo that shares as many features as the Caro-Kann and the Slav. All the other defences against e4 lead to unique pawn structures and piece constellations that aren't easily reached from d4/c4-openings. 
Just playing the same move against e4 and d4 either leads to completely different openings (Indian Defences/Alekhine, Sicilian/OldBenoni, French/Whatever) or exactly the same defence (The Modern). 
That being said, there are some popular opening-combos, but they usually own their popularity to a similar attitude or character of play. 
One such combo would be the King's Indian and the Dragon. The obvious similarity is the fianchettoed bishop and the aggressive attitude. 
Another might be the French and the Nimzo-Indian. Both are rather strategic setups with counterplay on the queenside. 
The Queen's Gambit declined and 1…e5 would be another sensible combination. The attitude is classical: Equalise first, play for a win later.

user9684: The Pirc, modern, and KID.  If you attack the center with ... c5, it could turn into a Dragon Sicilian pawn structure, but it is safer because both players have castled, normally kingside, by the time the break has occurred.

3237: <p>One well known very good combo is the Caro-Kann + the Slav:</p>

<ul>
<li>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.</li>
<li>They tend to lead to roughly similar Pawn structures.</li>
<li>On average they both tend to lead to positional, quiet and strategic games.</li>
<li>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).</li>
</ul>

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

<p>Enumerate as many combos as you can. But I am only interested in combos where both openings are sound.</p>

<p>And if possible also explain why exactly the openings work well together.</p>
 4362: <p>I don't think there is a single other opening combo that shares as many features as the Caro-Kann and the Slav. All the other defences against e4 lead to unique pawn structures and piece constellations that aren't easily reached from d4/c4-openings. </p>

<p>Just playing the same move against e4 and d4 either leads to completely different openings (Indian Defences/Alekhine, Sicilian/OldBenoni, French/Whatever) or exactly the same defence (The Modern). </p>

<p>That being said, there are some popular opening-combos, but they usually own their popularity to a similar attitude or character of play. </p>

<p>One such combo would be the King's Indian and the Dragon. The obvious similarity is the fianchettoed bishop and the aggressive attitude. </p>

<p>Another might be the French and the Nimzo-Indian. Both are rather strategic setups with counterplay on the queenside. </p>

<p>The Queen's Gambit declined and 1…e5 would be another sensible combination. The attitude is classical: Equalise first, play for a win later.</p>
 9684: <p>The Pirc, modern, and KID.  If you attack the center with ... c5, it could turn into a Dragon Sicilian pawn structure, but it is safer because both players have castled, normally kingside, by the time the break has occurred.</p>
