Receiving on multiple UARTs is ok. Sending is going to be complicated. In addition to the collision problem, there's a hardware issue. At UART holds the transmit line at a fixed level when idle (sorry, don't remember if it's high or low) so it's not just a matter of connecting all the transmit lines in parallel.
In the shadows of my mind, I have done this before so I could see data from several devices at once. IIRC, it involved diodes and pull(up or down) resistors.