the benoni comes to my mind. you could even invite a transposition to the dragon by playing 1 g6 2 bg7 and 3 c5 when possible. admittedly this is the hyperaccelerated or accelerated version but still a dragon. i'm not aware of any other opening that would allow an unobstructed fianchettoed king's bishop as in the dragon, if that's what you are seeking to get.
Opening against d4 similar to Sicilian dragon against e4
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Benonis and Benkös have the same pawn structure for Black and can lead to active positions, but still the play is quite different from a dragon as the center is not open.
Kings Indian Defense
Jan 21, 2021
0
#5
the difference between the benoni and sicilian is that white often tries to stomp you in the center in the benoni. i think thats because white gets a pawn on d5, so black cannot play d5 to counter strike at White's center. after d4, if black plays c5 white can comfortably play d5 usually, which is why its harder to get sicilian like positions. so i dont think you can really get a position that is just like the sicilian after d4, but the Kings Indian is very sharp, like the sicilian, and many grandmasters who play sicilian also play the KID
I am looking for a black opening against d4, I like to play the Sicilian dragon against e4 and am looking for something that maybe has some of the same ideas or style. All suggestions welcome.