The only thing made that is similar to what you are looking for was the Classe Sigma 2200i integrated amp. It has 4 HDMI 4K inputs (only one supports HDCP). However, the audio over HDMI only supports 2-channel PCM, so you will need to configure your sources to send only 2-channel PCM. This would be a used item. Nobody has it up for sale now though.
Otherwise, you'll need to do an AVR or a HT Processor with a separate amp.
Otherwise, you'll need to do an AVR or a HT Processor with a separate amp.