That's not a side dish. That's a main course competing with the host for your own ego purposes.
You did that at my house, you wouldn't be invited back. In fact you might even get shown the door. It's an (*) move, sport.
Now, if you were specifically requested to bring another entree or that particular dish, then fine.
I knew a jerk that when he'd get invited to cookouts, he'd smoke his own ribs - knowing that ribs were being served - just so he could show up the host. Did that at least 3 times at different houses in my old neighborhood. He - and his entire family - were never invited back to anything. That's just rude.
As to what I'd bring, I'd grill some eggplant, zucchini, shrooms, artichoke and peppers, cube up 2-3 different cheeses, throw some fresh basil on it and maybe include some salumi, and voila, antipasto.