Using a MIDI connector both as MIDI In and Out (not simultaneously)
I suggest you have a look at the 4051 or 4052 chip (datasheet). The 4051 is a 1:8 analog multiplexer while the 4052 contains two 4:1 multiplexers. So basically it allows you to switch one pin on your Arduino to any out of 4 or 8 MIDI circuits.

In the case of TX, it's really simple. You just need a pullup resistor on each output so that the pins don't float when not switched to.

In the case of RX, you have to make sure that you don't miss any transmissions. If your MIDI sources are not sending simultanously, that's easy as well... but probably they are. In that case you cannot use an existing RX UART. Since MIDI is very slow, you could still switch back and forth between the inputs and catch all the bits (you would be writing a software UART then). But if you're not short of pins, it would be much easier to just use SoftwareSerial for one input.