Can I buy a second base for my Carseat?

Unless the restraint you purchase is a 'Carrier' or 'Capsule', you cannot get additional bases.   

'Carrier' or 'Capsule' are specific restraint designed for newborn use, normally for 0-6mths or 0-12mths and are designed so that the seat piece can be removed and carried from the car leaving the base behind.

All other restraints like convertible carseats e.g. restraints that rearface and then convert to a forward facing carseat, are complete units that must be completely uninstalled and reinstalled when removing or changing cars, you can not remove the base from the seat.