Set-up based e4 openings for white

there is the king's indian attack using 1 e4 as a move order. there's also the reversed philidor with e4 d3 c3 be2 nf3 and so on. maybe also e4 d3 and c4 but i think this is lame if you begin with 1 e4 and if you're going to play like this it's better to start with 1 c4 anyway. however, don't expect to be undisturbed too often.
you're supposed to welcome early confrontation though, as that is the spirit of 1 e4. you push an unprotected pawn and invite aggression.

There exist no "systems" that work against everything:
London - 1.d4 g6 2.Nf3 Bg7 3.Bf4? (Even London guru Lakdawala says this) d6 4.e3 Nd7 (or 4...Nc6 is also strong) 5.h3 e5! =/+
Modern Defense - 1.e4 g6 2.d4 Bg7 3.c4 d6 4.Nc3 Nc6? (4...e5?! +/-; 4...Nf6 is now a King's Indian) 5.d5 with a clear advantage for White
English Opening - 1.c4 e5 2.g3 Nc6 3.Bg2? (Always answer ...Nc6 with Nc3, after 3.Nc3 f5 4.Nf3! Nf6 5.d4 e4 6.Nh4! - With a Bishop on g2, the Knight would get trapped h 3...f5! 4.Nc3 Nf6 and White has nothing!
So no, nothing works against everything. The KIA sux vs 1...e5, 1...Nf6, 1...d6, 1...g6, and is not even possible after 1...d5.

Closed Vienna maybe but you'll find yourself on the end of some pretty vicious attacks if you're not careful
I always feel like the nature of 1. e4 openings is not the same to the nature of 1. d4 openings. Where 1. d4 middlegames tend to be more focused on structural advantages (QGD: bad bishop for black; Nimzo: space advantage and bishop pair for white but at the cost of a pawn weakness), 1. e4 openings tend to be more focused on dynamical play (there are many gambits after 1. e4 e5; vs Scandinavian white often has to be quick with a lead in development and the initiative versus an otherwise sturdy black structure). Therefore I feel your question doesn't really fit the nature of 1. e4 openings. And I can't really think of a one-setup-fits-all opening or an opening that is even that much setup based. For setup openings, you might be better of with 1. d4 or 1. c4/1.Nf3.
there is the king's indian attack using 1 e4 as a move order. there's also the reversed philidor with e4 d3 c3 be2 nf3 and so on. maybe also e4 d3 and c4 but i think this is lame if you begin with 1 e4 and if you're going to play like this it's better to start with 1 c4 anyway. however, don't expect to be undisturbed too often.
The "reversed philidor", man that is just sad. The opening is weak enough for black never mind white.