In Western classical music theory classes, progression writing is typically focused on the voice-leading principles of Tonality, in the context of four-part vocal writing. So cadences, for example, are voiced to preserve the smooth movement of each voice (pitch) to the next. (Jazz and Pop music are looser in this regard, but tend to follow the same principles.)
You can change the voicing/inversion of any chord, but the subsequent chords would also change to preserve the voice leading. Taking your
Ib - ii7b - V - I in the key of C Major, a standard arrangement would be:
But let's say you prefer
ii7b. If you change only that one voicing, you get this:
To get a "correct" solution, you would have to change, at least, the
V chord. For example,
Ib - ii7b - Vc - I:
It's okay to double any pitch(es) in the chord, but -- again for "correct" voice-leading -- it's best not to double pitches that have strong movement toward another particular pitch in the next chord. For this reason, you should near always avoid doubling a leading tone (e.g., the third of a dominant chord).
For a (vastly) more detailed description, see Steven G Laitz. 2008. The Complete Musician. Oxford University Press.
For anyone unfamiliar with the notation used in the three examples above, it is equivalent to:
I - ii[6-5] - V - I,
I - ii - V - I, and
I - ii - V[6-4] - I.