Parallel batteries work OK, usually you stick to using the same type/brand/ratings to get all characteristics as equal as possible.
We’ve even charged each battery individually, then connected them in parallel, discharged slightly then charged again to ensure they are about as equal as possible before flying.
Too many Y cables and connectors all introduce more resistance - and in this situation where you’re likely drawing tens of amps at relatively low voltage, every micro-ohm makes a difference.
The key thing will be spending some time in ecalc and check if the extra batteries (mAh) actually give you anymore flight time because of the additional weight. https://www.ecalc.ch/xcoptercalc.php
In ecalc battery weights are per cell, so you could weigh you battery and divide by 4 (4S) and use that value for cell weight.
It could be OK if your copter is already overpowered. If the aircraft is underpowered or already “just right” for 1 or 2 batteries, adding more batteries could compromise stability. So you could easily end up with slightly more flight time on windless days, but crash as soon as there’s a gust of wind.
That should be fine so long as your connectors are all in good condition and wiring is suitably sized. Probably balance charge each battery individually, then join them all up and do a final fast charge or similar to make sure they’re not going to be fighting each other.