For one system that can be used in both e4 and d4 something with 1. g6 is probably your best bet. The black lion defense seems like the most attractive line in this setup I'm aware of, I haven't looked deeply into it but you could take a look. I think you'll have to play other lines in the modern or a KID in conjunction though if white plays something like c4.
Otherwise the way it usually works is players play separate openings against d4 and e4, but the openings might pair together in a way that makes sense... they may have some common pawn structures or similar piece setups. One obvious example would be playing the caro-kann + the slav or semi-slav.
Generally when you choose a your responses to e4 and d4 you should consider how the two lines combine to handle the Reti / English as well. There was a recent thread on this topic - Which 1. e4 and 1. d4 defenses should be paired together - Chess Forums - Chess.com
There are several opening systems for White such as London and Colle system etc.
Is there an opening system for black?
If yes,what will be your suggestion for black opening?