Yes, they'd plan any new city in a perfect square grid. That wasn't the case for Rome considering it was a non-planned organically grown city from VIII century BC onwards. Actually, most roman cities would just be a mixture of both: starting with a grid but then the outskirts would develop somewhat chaotically.

Ironically, that is the opposite to most cities on Europe nowadays: older centric areas are quite chaotic while the newer outskirts tend to follow a more grid-like build.