Many continuo manuals (both historical sources and modern treatises) are careful to point out that a continuo realization should be contrapuntally correct, i.e., one ought to avoid parallel fifths and octaves in the extemporized parts, as well as other voice-leading mistakes. (With some amount of license allowed in very full-voiced textures.)
However, such prescriptions only seem to apply to the internal consistency of the continuo realization. Most continuo manuals that I've seen only show music examples for the realization itself, and not for the composition as a whole. For that reason, I'm wondering how the realization should interact contrapuntally with the other written parts of a composition.
Suppose, for example, that we have three string parts (2 violins, viola) above a continuo line. If I want to play a four-part continuo realization, should the resulting seven-part texture be correct contrapuntally? That seems almost impossibly difficult to me, especially if it has to be extemporized. Or am I allowed to double in the right hand one or more of the written parts, so that we effectively get a less than seven-part texture?
I find this a rather confusing aspect of Baroque musicianship.
Edited for clarity.