It would help if you mentioned your budget.
Three HDMI outputs tend to be available only in the most expensive receivers and preamp/processors. A much less expensive HDMI switch might (or might not) be more appropriate. In contrast, some amount of room/speaker equalization usually is available in all but the least expensive models.
At least a couple of the high-end Denon receivers, for example, have three HDMI outputs: two for the main zone (TV + projector) and one for zone 2. Note, however, that if the zone 2 TV supports only stereo (as most do), then when it's powered on only stereo is available in the main zone, too. The HDMI protocol causes the source players to limit their output to be compatible with the least capable display device.
Most modern receivers don't just auto-calibrate the over-all sound level, but also include room equalization. They equalize the output at multiple frequencies in order to produce accurate sound in your listening environment.
Marantz SR7009 avr + MM9000 amp --> Atmos 7.1.4
Fronts=NHT 2.9+AC2, FH+TM=DefTech PM1000, LCR+TM amped