Most auto tranny fluids contain friction modifiers. These provide extra slip to soften the feel of the shift. Friction modifiers are consumed with useage, so these modified fluids must be replaced on a scheduled basis, usually every few years. Type F contains no added friction modifiers and tends to last a very long time.
Even small amounts of friction modified tranny fluid in a type-F tranny will soften how a tranny shifts, and if the tranny is specifically calibrated for type F it may slip excessively with the modified fluid. On the other hand, it is usually OK to add a small amount of Type F to a tranny that requires modified fluid, as it won't change the shift character in any noticeable way.
It might be wise to drain the fresh modified fluid, fill with Type F, run it a while, then drain and discard the fresh Type F (since it will now be mixed with friction modifiers), then adding another batch of new type F fluid once again. Also, filling while draining does not completely eliminate the old fluid, so it might be best to drain the tranny as much as possible before adding any fluid.