The BrickPi+ uses the RPi UART (/dev/ttyAMA0) and each AT has an address (1 and 2) in the used message protocol.
Is it possible to connect a PC to this UART while RPi is using the BrickPi+ to allow an independent communication between the RPi and this PC?
I whould configure the UART in the PC with the same characteristics (speed, bit stop…) used by BrickPi+
And I whould limit the same messages communication protocol with the same form as BrickPi+, but using different addresses ( 3 for the RPi and 4 for the PC, for instance)
Is it possible?
It’s probably possible, but I would recommend using IP for communication between RPi and PC. IP sockets work well.
as the OP wanted to use a serial UART protocol:
I would suggest to use USB then, both on PC and the Pi, attached to an CH340 FTDI USB-to-serial Converter each and wired via RX/TX as usual.
Then one would have an additional, independend UART port, not interfering with serial0 to the BP+ any longer.
I personally think a different route would be simpler. You could communicate through USB, or web sockets through a network.