I could not find a forum entry on 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3 Be7. It's a main line, second only to 4...Bc5 in popularity. 4...Be7 was recommended by Martin Lokander:

https://forwardchess.com/product/opening-repertoire:-the-open-games-with-black?s...

The play can continue 5. O-O O-O 6. Re1 d6 7. a4. At this point Lokander prefers 7...Kh8 to the more frequently played 7...Na5.

I am curious about treating this like a Chigorin Ruy Lopez. In my notes I have 7...Na5 8. Ba2 c5 9. Na3 Nc6 10. c3 Be6 11. Be6 fe6 "slightly more pleasant for White." Continuing on a little, 12. Bd2 a6 13. h3, black seems to have good chances in an unbalanced game (13..h3, 13...Qe8, 13...Rc8).