No
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no problem doing the S/E add-on in a primary trainer
Correctamundo! From the Commercial PTS:
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Aircraft and Equipment Required for the Practical Test
4. be a complex airplane furnished by the applicant, unless the
applicant currently holds a commercial pilot certificate with a
single-engine or multiengine class rating as appropriate
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Position: PA-44 Left
Posts: 177
Of course, that means you'll have to change your data ...
again.
Seriously, it's a class add-on (look it up in FAR 61); very easy to do.