On Arduino Mega, if you really need 6 serial ports, and 2 of them could run at relatively slow baud rates (eg, 9600 or maybe even 19200 baud)... you probably could use 2 copies of AltSoftSerial. You'd need to make another copy of the library, change the name to something like AltOtherSerial, and edit its copy of config/known_boards.h to use the other timer.
Mega actually has 4 of those timers, so in theory it would be possible to have 4 copies of AltSoftSerial working simultaneously (at slower baud rates), for 8 serial ports working simultaneously. Unfortunately, 2 of those 4 timers can't be used, because the input capture pin for those timers is not brought out to any location on the board. However, if you only wanted to transmit and never receive, you could make modified copies of AltSoftSerial that only transmit. It's the receive pins that aren't available on Mega's PCB layout.