If you want to support d4, a better way to play is via the Italian move-order 1.e4 e5 2.Nf3 Nc6 3.Bc4 and here, on 3...Bc5, to play 4.c3 Nf6 5.d3 or against 3...Nf6 to play 4.d3 and 5.c3.
I've looked into those lines, and want to give those a try as well.
What are your thoughts on the Kings Indian Attack set-up? I like the idea of Nbd2 adding an extra defender to e4 in the beginning, with future jumps kingside after Rf1-Re1, i.e., Nbd2-Nf1, followed by Ne3, Ng3 or Nh2. Quite a journey.
I got this idea from some of Bobby Fischer's games. I've heard that Fischer had a problem at one time with the French Defense, so he would play a KIA against it. This is one of my favorites, especially how Fischer makes use of both knights on the kingside.
I usually play 1.e4 2.Nf3 3.Bc4, the Italian. In the past few days, as an experiment, I've been playing 1.e4 2.d3. Hardly ambitious or agressive. However, I do like playing with different pawn structures now and then, and this one is quite different, for me.
It can lead to a Kings Indian Attack structure, but doesn't always need to go that way. I don't like playing on auto-pilot, and may try the Reti next (1.Nf3), as it offers lots of flexibility.
I find Nbd2 of great interest right now, as opposed to my usual Nc3. It affords me the opportunity to push my c-pawn early on, when it makes sense to do so, with a d3-d4 break in the center, like in the Guioco Pianissimo, not to be confused with the Guioco Piano.
I am surprised at how popular the Guioco Pianissimo is at the highest level of play (d2-d3), more so than d2-d4.
Here's my most recent game played with a c2-d3-d4 pawn structure with lots of my own annotation/thoughts and some engine analysis.