I have done that before. My main remote power supply is a 12v 2,000w samlex on top of 60ah of LiFePO4 prizmatic cells.
The lithium battery attached to the power inverter would supply the Lions share of power then the lead acid would provide 20-30 amps through jumper cables under load, then 10-15 amps during recharge.
Bus this was an ice car with a rather anemic alternator.
The samlex has a built in breaker that triggers if I connect a 9 inch grinder or skill saw with out a varriac.
"THE ABOVE POST CONTAINS MISLEADING AND INACCURATE INFORMATION. PLEASE CONSIDER IT OPINION, NOT FACT". -someone who I offended and is unable to produce the facts in question.