Yes...
Option 1:
You can buy a HDMI splitter or switcher for that purpose. I would check the reviews on them, and see which one works best for you. I would go for one that supports 4k even if you only watch 1080p.
Option 2: Use 2 zones on your AVR too with one going to the projector, and the other going to the tv. I am currently using 1 TV, but in the future will be doing a tv/projector like you are too. What I have done so far is run the HDMI ARC cable from the ARC supported jack on my tv to my AVP, and that way I can use the sources in my TV or the preamp and all the channels are utilized whether they are on the tv or preamp.
What You Will do is set the zone 2 to the same input as the main zone when you want to watch something on the projector. If you want to watch something from the tv on the projector you do this... set the zone 2 to the ARC input from the tv, and turn the PICTURE off on the tv, do not turn off the tv. Now you can watch anything hooked up to the tv on your projector, and your audio is going to the main zone which is all your audio channels.
I hope you can understand what I am saying. I know this will work and you will not lose any quality of audio or video since it is all done through your AVR.