Two ARC connections to Amp for home theater

Hi all.  I would like to install a projector screen and projector for my pergola that points to the pool. I currently have a television in the Pergola that is connected to an Amp through HDMI. I would like to keep this connection but also connect the projector to same Amp.  The ultimate goal would be for the amp to play audio from whatever source is sending audio.  At any given time I would only be using either the projector or the television, but not both.  Is this doable with some sort of HDMI splitter?  If so, do you have any recommendations for a splitter?