The major problem the Spartans face was their equal inheritance laws. Citizen status depended on being able to pay for your communal mess rations without having to do work. This meant land ownership, and as land was divided among heirs, it became harder for them to pay for their rations, so the number of citizens declined. Impoverished heirs would often have to sell their lands at a loss, so the wealthy few at the top of Spartan society could accumulate gigantic landholdings, while the former Spartiates could never regain their status as equals. You'd want to somehow give the Spartans primogeniture, and possibly a cap on how much land a Spartiate could hold.