You can't run more than one com3 at a time, but you can|
switch between pins. I do this all the time. I have used
a BX24 to display a menu on LCD. The data arrives on
Com1 and goes out to Com3. But I have many other devies
attached too, like an IR decoder, GPS, sensors, etc. If
you design carefully, there is no reason why you can't
do it by switched the Com3 around to different pins.
Think about how much time is actually used to display
characters on the LCD. Not very much.