Two devices on one UART/Serial
It's certainly possible to multiplex a UART port, yes, though you will need extra hardware to do it. You will need:


A multiplexer to select between the two RX lines and feed the right one to the Arduino's RX pin
A demultiplexer to select which of the devices to send the Arduino's TX pin to.


"Analog" (de)multiplexers (e.g., CD4052) may be the simplest option since they can work in both directions. Another alternative would be combinations of tri-state buffers and glue logic to control them.