I wouldn't recommend it. I know when SU changed to the new firm foam ink pads, they had to reformulate five colors because the old formula for those five colors don't work on the new pads. (and that is with the same brand, same color!!!)
Just my opinion though. I would ask in the general section to see if anyone has ever done this and what the results were.
I have reinked with different color and brand, but always the same type of ink, mostly dye inks: used a different brand(Dots) of a green ink I got at a garage sale on a fading(old) Stampinup green that I did not have a refill for. worked great, color was similar enough it didn't make a big difference and blended in well. All I did worked well and just had the blend the colors together, which goes by quick if you stamp a lot!!
Cyndi, I would recommend to not reink using different ink. I agree with the other comments that different inks have different properties and mixing two different inks together may give you results that you will not be pleased with.