One possibility is subs that have a line out and you can daisy chain. Receiver outs go to first sub and out from that one to the next. Any amplitude loss can be compensated with sub volumes.
Who told you about needing an amplified splitter? Your receiver is your line level amplifier. You adjust volume on the subs. The only real issue is noise due to cable length but 20ft isn't bad unless it's a very noisy electrical environment.
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