Most current rule sets will have the second and third lines running from the morale effect of seeing the first line broken.
I have used Punic Wars period legions in two lines, but we don't know how it actually worked - and even whether there were effectively three lines or a staggered array, or even whether the lines closed up to present a solid front versus some opponents or retained gaps vs others.
It also seems to me the obsession with Romans is detrimental to ancients rules in any case. I suspect a hangover from older British rulesets written by pukka chaps, whose education was training for exceptionalism and empire, with Roman virtues lauded and Roman heroes venerated. It's still a thing with the view of the 'Western Art of War' or the clash of civilisations.
Me, I would like to know how 3rd & 4th Century Roman armies consistently lost to the Sasanians. The Roman annals are noticeably terse, and it is very hard to replicate with current rule-sets.