Short answer is, not a good idea because the existing current UPS charger of yours can charge small battery quick enough to maintain its full charge basically. If a bigger battery is being replaced, it will probably take long time to charge and charger may overheat or burned or error out because it cannot charge battery back to full again. Now some people said they take the battery out to do a full recharge on a car charger, that may work but how do you unplug it from a working UPS currently in use? just disconnect the wire? well that may or may not work, you have to experiment.
Most UPS backup battery power don’t last more than 3 years, some 3-5 years the most then the battery will go bye bye. Most SLA or sealed led acid battery don’t last long, most will last less than 3 years even if you don’t put a load on it. The led acid will degrade over time even with just maintenance charge, don’t think that you charge it and then let it sit somewhere and months later use it, it will still have that full charge, no that’s not the case for all batteries.
I have done many experiment in the past with this and the result as I have stated above. I know that you’re trying to save money or be cost effective and try to connect a bunch of batteries in parallel to get longer hours of usage during power outage, but that’s not effective and further could burn your UPS charger when power goes back on. Now disconnecting the batteries to charge on a car charger is not efficient or practical because you’re interrupting current devices connected to that UPS power. The best way if you want bigger battery is to buy a bigger ups or maybe a powerwall, it’s much safer and more reliable than you trying to hack current UPS. You can probably get away with one car battery, but more than that I think you’re in a lot of risk that is not worth it.