Multiplexing UART

Hi Guys!
I'm working on a board that needs to use an USB and RS485 interface.
I'm using an ATMega644 MCU.
CH340G for my USB to UART, and MAX485 for RS485 interface.
75HC4052 for Multiplexing via two interfaces.

So my questing is, how to make it the best way so I can use two interfaces at once.

Note: I can't use different MCU, Drivers, Multiplexers and etc.

My best idea was to use hand shaking (Flow control) procedure on CH340G the CTS and RTS pin,
and when I switch my MUX to read USB, I confirm that I'm ready to read from my USB via CTS pin.
When RTS is low I can see that serial port is open for some data exchange. But the problem is, when communication is opened on PC, I will only work with USB, I can put RX from RS485 on interrupt, but i don't have that many pins left :smiley:

Something is telling me that this is not the best way, it can be better, so I'm asking you guys for help.
I'm sure that you are all here professions and can give me a hint very easy.

Thank you in advance.