No. Well, sort of. Midi isn'the designed for this. But it is possible within some strict limits to do this.
The limits: There is only one pitch change message per midi channel. The result: Single note melodies with no overlapping notes could be retempered on the fly with software. Or, multiple midi channels could be used (which is how many guttar synths do it: one midi channel for each string), allowing independent pitch change messages for each note of a chord, for example).
Potentially the best solutions for changing the temperament of midi playback is to either sample each note yourself, or to use a VSTI that allows you to dial in the precise pitch shift for each playback note. This 2nd option is much more versatile, but few sample player VSTI's offer that option.
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