Decisions decisons, speakers or an amplifier

Speakers. Too much spent on electronic upgrades.

I agree that upgrading to 3.6's will give you more bang for your buck than an amp upgrade.

If your room can handle them, 3.6's

I don't know much about the Parasound. My personal approach would be to upgrade the speakers to something that will benefit from every upstream upgrade for a while, and I think the 3.6's would do that. My guess is that the Parasound isn't sufficient for them, but that buying them first would give you a serious "Wow!" factor, and that future upstream upgrades would provide continued smiles.

I haven't ever had a pair of Maggies, but I've heard many references to them working extremely well with Acoustic Research amps. As always, so much depends on your room size, acoustics, and musical preferences.

The point brought up by Kthomas is important 3.6's need power to shine.
They are big and need space to perform properly.
3.6's will provide you with much better bass and if in the future you can also upgrade amplification you might be surprised with them in this area. (Not their forté, but good)

A fellow audiophile has 3.6 powered by Rogue M-120 monoblocks in a large room and sound very good. Source is Northern Star transport and DAC

You will love the 3.6s. I agree they will almost surely lead you to ugrade the amp too but the Parasound will be great for the time being. Enjoy!

The Parasound Halo A51, putting out 250 watts per channel, has plenty of gain for the speakers. I would vote for the 3.6s if you are ultimately headed in that direction. As for amplifier upgrades later, you might consider Parasound Halo JC1s or perhaps tube amplification. The JC1s will be cleaner, sweeter and more musical and rhythmic than the A51. You could use the A51 for the bass if you choose to biamp the 3.6s, and in the meantime if you have the other channels of the A51 available, you could use four channels of it to biamp the speakers. Disclaimer, I am a Parasound Halo dealer; I hope this post helps you. Good listening!