Looking for a Converter/Charger that does both AGM and Lithium

I need to upgrade our current single stage charger; would like to only have to purchase this item once. Do they actually make one that can work with all battery types?

Yes, there are many that do this. Depending on the voltage and capacity of your battery bank, and your source for charging (grid, generator, alternator) I’m sure you can get multiple recommendations here.