Yes, putting the panels in parallel will let you move more water through and that will provide more heat, but as Carl mentioned the plumbing is more complicated (the diagram I drew in this post shows a parallel configuration that equalizes the flow to be the same for all panels). It won't be 3 times as much for a variety of reasons, but it will be more. You can never get more heat from these panels than the amount of solar radiation that hits them. There will also be a limit as to how much water you can move since it is recommended not to exceed a flow rate of 10 feet/second in pipe and with 2" pipes that's around 100 GPM, but you probably aren't at that point and any excess can go to a bypass to your pool. I also don't know what sort of pressure these panels can take without leaking, either, but as Carl says you can try configurations to maximize heating until you reach a limit or problems occur. By having a valve to allow for a variable bypass, you can tweak the flow rate through the panels for maximum heating without getting leaking or excessive flow rates.
If your 4x10 and 4x20 panels are similar to the FAFCO ones I linked earlier (or to this link which is for 4x10 and 4x20 panels designed for above ground pools so may be more similar to what you are using), then they have a maximum recommended flow rate of 8 GPM per panel and a maximum pressure of 30 PSI (intermittent up to 45 PSI). With your 3 panels hooked up in parallel, that would mean 24 GPM maximum recommended flow rate. But again, you can try more but may have them leak at some point. Just remember that at 8 GPM per panel you are already getting 90% of the heat you can possibly get out of the panels so at most a faster flow rate will only get you 10% more heating (this is different than Carl's situation because his solar panels are completely different as decking where the flow rates were not even close to the efficient range with so many panels hooked up in series). Depending on the panel, it is possible that too high a pressure (to get higher GPM flow rate) might cause a panel to burst or break which is why I think you should look at the specs for the specific panel you are using and not exceed the maximum flow rate that they specify or certainly not the maximum pressure they specify.
Richard
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