As a role of thumb, adaptation rates --wherein I presume you are referring to sensory prediction error driven learning - are typically lower with an increasing number of targets.   However, this is a tricky question because the secondary question is whether or not the same perturbation is applied to all targets or not.  Non-surprisingly, introducing another target with an opposite perturbation leads to anterograde interference.  Though, the cause of such interference is still debated and may not necessarily imply a different learning rate (consider the paper by Lee and Scheighofer, 2009). I am going to self-promote an EEG paper on this topic we just released, too.  

The overall answer to your main question relies on answering the other unknown which is, can people up/down-regulate implicit learning rates from sensory prediction errors.  If not, then conditions that look like altered rates are due to unaccounted for factors. Otherwise, the Bayesian (if you will), might argue that people up/down-regulate the learning rate as a function of confidence/uncertainty/precision in beliefs (choose your nomenclature 'poison'), which might be affected by the number of learning targets (this is also akin to the question of whether generalization is local or global - Donchin and Shadmehr paper linked).  

Cheers,

Justin Fine

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Thank you very much Justin for this clear answer!