Can you mix and match battery's say a starting that that is a wet cell and an accessory battery that is a AGM or Lithium?
This is a single engine with your basic battery selector switch

You can, but should keep them isolated (not combined) from each other.

One decent article of many:
https://www.pysystems.ca/resources/a...a-single-bank/

The different battery types of different voltage potentials if all you have is a basic switch, I wouldn't recommend it. I have a Pro Marine charger and it has different charging profiles for each of these battery types. I highly recommend staying away from Lithium. I sell a specialized camera that detects smoke and fire and I am getting calls from Lithium battery manufacturers who want to use our cameras to monitor battery storage and vehicles because they can burst into flames.

Should not be done due to different charge rates. It will work, but over time there can be issues

Lead Acid 12.7V
AGM 13V
Lithium 13.4V

Edit: Just bought a ProMariner 50 amp 3 bank charger and would not recommend them.

get rid of the old lead/acid battery for starting
very undependable outdated battery
and run 2 agm and get a battery charger that is agm capable
last longer,,,deeper cycle for continous usage,,,,,lots more dependable set up

You can use both types. Just don't run your battery switch in the both/all position due to reasons stated above.

It is far easier to just get matching batteries and not have to worry about switching your selector all the time, and if you have or put an on-board charging system on you avoid all sorts of hassle. I recently changed over to Odyssey AGM batteries and love them, a bit more expensive than some (about $400 each), and then put a charging/maintaining system on that I hook up when I am in the slip at the lake.

I would avoid lithium batteries completely. I have a lot of r/c stuff and have seen several lithium ion packs catch fire. A bit different technology in the big vehicle batteries, granted but...no way would I have one in a boat or car/truck.

when I got my boat it had the very set up you are describing(lead acid and AGM with perko switch) I ran it for about 5 yrs with no problems but replaced the AGM with lead acid when it failed. I do not have an on board charger. I think they should match.