You do realize that the transistors will propbably invert the signal it passes on to the zif? They will not be a simple/make break between the arduino pins and the zif pins. But without seeing what is going to be plugged into the zif it's difficult to suggest a way to do what you may be trying to do?
But yes you can drive multiple base resistors from a single output pin.
I do not realize that.
What I'm trying to do is see if it's possible to replace the DIP switches on my ATtiny/ATmega programmer shield.
The way it works now is you load the ArduinoISP sketch to the Arduino, plug the shield in, and then there are different 3 banks of 6 DIP switches (and some jumpers) that you flip based on the microcontroller you want to program. The reason for the switches is because the GND, VCC, and SPI pins on each type of microcontroller are different.
Ideally I'd like just one switch, so I figured the best way to do this would be with transistors. I tested a bit using the transistors between some of the SPI pins and they seemed to pass the signal through just fine, but I haven't tried with all of them at once.