For pins 3 and 4 on Teensy 3.1, no.
There are 3 real hardware serial ports. Their signals can be reassigned to certain other pins, but not 3 or 4. For example, Serial1 can alternately use pin 5 for TX1. Since this is a function of the way Freescale designed the chip, only a few alternate pins are available for specific ports.
The AltSoftSerial library can give you a 4th software-emulated serial port. It's not nearly as efficient as the hardware ports, especially Serial1 and Serial2 which have built-in FIFOs, but it does work well. Lower baud rates, like 9600 or less are best. It can work faster, but the cost is quite a bit of CPU usage. With AltSoftSerial, the default is receive on pin 20 and transmit on pin 21. That library does have a config file you can edit, to reassign to other pins. But only certain pins are possible: 5, 6, 9, 10, 22, 23 (because AltSoftSerial uses a timer which connects only to those pins). Pins 3 and 4 aren't on that list.