You can run multiple chargers as long as they play nice with each other, you won't hurt the batteries or the chargers, but if there are differences in the charging voltage , one might decide the batteries are charged and reduce its output, sensing the higher voltage of the other charger and deciding the batteries are near full, it depends on the electronics of each device, this happens more with external automotive style chargers then converters, the factory built in converters are more like DC power supplies than smart chargers, and should work ok in tandem with the lithium charger, the additional 20 amps seems like a good idea, definitely something i would try