In theory it would work with any number of strips in parallel - as long as the drive of the Arduino is strong enough to get the signal to all of them. The data pins themselves take basically zero current, it's the stray capacitance of the wires and pins that has to be overcome.
2-4 of them will no doubt work.
5, 6 of them, probably as well.
More than that... no idea where the limit is. Try it. Maybe you have to start buffering the signal, a 74hc04 should do fine. Two inverters in series for each buffer. That way you can get to really big numbers of parallel strips.
Make sure your power supply is up to the job. If you have multiple supplies, share grounds, NOT +5.