The 3700 has 9 amplifiers and 11.2 preamp channels. I would suggest using them instead of an external amp. At least in the beginning. If your sound levels are usually in the 70-80db range it's very possible you will not require an external amp.
However, many of us can't help but want to try external amps. In most cases, the sound quality is unchanged but the receiver may run cooler as a side effect. If you are going to run all 9 channels it's probably worth considering using a 5 channel amp on the floor units and let the receiver handle the Atmos. But again, I would try it as is. If it runs hot try the eco mode and if doesn't help enough the 80mm USB fan can be helpful too.
IMO, an amplifier for the three front channels should amply be sufficient for most situations. Most of the power demands in home theater concern the front channels, and surround including Atmos speakers receive a minimal signal compared to those main channels. The AVR should normally be adequate to handle them.
Unless the listening distance from the main speakers is greater than average, let's say more than 12 feet, the OP listens at high loudness levels with low sensitivity speakers, in most situations an AVR should be adequate to drive all speakers. Driving speakers in average conditions requires only a couple of watts even for front channels.
Here is a nice calculator to find out how loud an AVR can output sound:
