A battery system includes: a first positive terminal; a second positive terminal; a negative terminal; switches; two battery modules, each including three strings of battery cells that are configured to, at different times be: connected in series and to the first positive terminal via first ones of the switches; connected in parallel and to the second positive terminal via second ones of the switches; and disconnected from both of the first and second positive terminals; and a switch control module configured to: determine state of charges (SOCs) of the strings of battery cells, respectively; determine, using model predictive control, periods of phases, respectively, to balance SOCs of the battery modules; determine, using model predictive control, periods for the strings, respectively, including setting one of the periods for one of the strings to be included in at least two of the phases; and selectively actuate the switches based on the periods of the phases and the periods for the strings of battery cells.