Republicans won't win more votes by being more like Democrats. That's going to lose them net votes because they will come out of their base.
They'll win more votes by being moderate in the right ways, while still maintaining principles. This means "fiscally conservative, socially liberal." AKA. Libertarianism.
Reagan already proved this model wins in America. Not only does it attract the conservative base, and attract moderates, but it also create division on the Democratic side (ie. Blue Dog Democrats)
Ehyeh asher ehyeh.
"You and I are told we must choose between a left or right, but I suggest there is no such thing as a left or right. There is only an up or down. Up to man's age-old dream – the maximum of individual freedom consistent with order – or down to the ant heap of totalitarianism." -Ronald Reagan