second opening?


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If I was you, I would experiment with various openings, such as d4, c4, Nf3, or Nc3.
Determine which opening you like best.
For your info, d4 is a very common opening.
Opening up with c4 is pretty positional.
I hope that this helps.
if you know only the Italian game for White then it seems foolish to me trying to learn another opening. Black is not forced to play 1... e5 and 2... Nc6 so I'd advice you to fill in the enormous gaps of your e4 repertoire before venturing into other openings

if you know only the Italian game for White then it seems foolish to me trying to learn another opening. Black is not forced to play 1... e5 and 2... Nc6 so I'd advice you to fill in the enormous gaps of your e4 repertoire before venturing into other openings
Agreed.
@robbondy, if you play the Italian, I'd first make sure I have both a response to the Two Knight's Defense (Could be the Knight Attack, the Open Italian with 4. d4, The Modern main line 4. d3 etc), and a response to the Giuoco Piano (Evan's Gambit or just 4. c3 5. d3, or 4. c3 5. d4 etc).
From there, I would get a response vs the other defenses that black can employ after 1. e4 e5, such as the Philidor and the Petrov
As I grew more comfortable in 1. e4 e5 positions, I would start to add in repertoires against the other main line defenses in the Sicilian (1. c5), the Caro (1. c6), the French (1. e6) and the more niche defenses like the Pirc, Modern and, Alekhine
If you really want to switch to 1. d4 instead, the Queen's Gambit will teach you the most about typical positions that derive from 1. d4
But switching from opening with one pawn to the other won't allow you to gain the experience in either to improve your opening play. 1. e4 and 1. d4/c4/nf3 etc have stark differences from each other
If you play 1. e4, I would stick with it unless you're having problems with it
Just my advice

On that level openings are not really important. That being said, if you aim to get to Italian game, there is no need to change your first move. 1.e4 will force you to play against many different responses eventually, and you will get some experience playing against 1. ...e5, Sicilian defense, Caro-Kann, French, Pirc, Modern, Alekhine, Nimzovitch...
Only if you really do not want to play 1.e4, after a while switch to something like 1.d4. Playing both makes little sense on sub master level. You can play 1.e4 for years and still be inexperienced in positions I've mentioned.

I assume you mean that the Giuoco Piano is your choice in 1.e4 e5 games, as there are many other choices for black after 1.e4 that you will have faced. The logical new opening move to try is 1.d4 as this usually leads to a different kind of game.
But don't try to become an expert on any opening yet. A little knowledge of the first handful of moves in the different variations you come across is sufficient until you understand the game better and can choose the variations you think best suit your style of play.
It is more important to learn to analyze positions and calculate variations. Play longer time controls so you have time to think about your moves and develop these skills. And it is far more useful to learn the simple endings (K+P and simple rook endings) than to study openings. You have probably noticed that many of the opponents you face at your level don't know jack about openings and frequently leave the book early on. Know basic principles and learn to reason out your own plans.