I'd suggest that all units produced in cities should cost 1 free population, and settlers 2-like in CIII. On top of it, unit and added city maintenance(for each new city) would bring with it corresponding lack of funds for research, culture (and faith).
So the statement that expanding quickly and producing settlers in great numbers would bring with it falling back in technological research, as well as culture penalties, but should definitely be possible.
For the imperialist players out there it would mean the possibility of creating a huge empire is there, but the fallback in tech and culture is certain as well.
Increased Corruption(CIII) and Number of cities maintenance (CIV) could also be added as penalties to expansion but to a much, much lesser degree than in those games, they were over the top.
So Expansion would have to equal/become Aggressive Expansion (much like throughout history), the need to create large armies to escort the settlers, to protect the new cities, to fight off hordes of barbarians and other, also looking to expand, civilizations.
Going for expansion would mean also becoming a warmonger, a technologically more, or less backward warmonger.
The more units you produce, civilian or military, the more population you lose from your existing cities, meaning a large empire would consist of large numbers of small cities, as compared to less expansive civilizations, with fewer but larger and richer cities.
The early (and mid game) wars for land and resources would intensify, letting players who enjoy combat strategize and enjoy the game more.
In civ1 and civ2, when you conquered a rival city, you gained a tech from that civ (if they had any you didn't own already), this could be added back to benefit expansionists (it could be a random tech), not just as a bonus to one tribe.
However, ancient Rome was huge, but at the same time a very advanced nation, so perhaps choosing the Militaristic-first, expansion of any non settled yet land after you conquer the cities of other nations philosophy could be more beneficial than the vice versa approach. Would mean less population loss. Also much less, or none, technology This (militaristic conquest and expansion) approach however, should bring with it the danger of coalitions of nations allying against such tribes and instead Golden Age an Age of Decadence.