It seems perhaps unlikely that a language would maintain a single special alternative suffix, to be deployed just in case the word to be inflected has in its derivational history another particular kind of operation. Indeed such situations do arise, however, a notable case from Sanskrit being the gerund, also known as the indeclinable past participle, or the absolutive:
(1) General gerund formation:
√bhū- ‘be’: ger. bhūtvā ‘[after] having been’ or ‘[when X] had been’ (MacDonell  1986: 137)
√jñā- ‘know’: ger. jñātvā ‘[after] having known’ or ‘[when X] had known’
(Whitney  1945: 56)
√vac- ‘speak’: ger. uktvā ‘[after] having spoken’ or ‘[when X] had spoken’
(Gonda 1966: 78)
Specifically, the gerund form is created in the general case by suffixing -tvā to the so-called 'weak-grade' root. When the verb lexeme in question is the result of prefixing a(n etymological) preposition as a pre-verb (PV), by contrast, the formation of the gerund is systematically distinct, involving a potentially distinct stem and an unrelated -ya suffix instead:
(2) PV-prefixed gerund formation:
ger. nipatya ‘having fallen down’ (ni- ‘down, into’; compare √pat- ‘fall, fly’: ger. patitvā)
(Mayrhofer  1972: 103; Whitney  1945: 94)
ger. vimucya ‘having freed’ (vi- ‘apart’; compare √muc- ‘release’: ger. muktvā)
(Gonda 1966: 78; Whitney  1945: 122)
ger. pratyāgatya ‘having returned’ (prati- ‘reverse, back’; ā- ‘(un)to, at’; √gam- ‘go’: ger. gatvā) (Deshpande 2003: 122, 428; Whitney  1945: 34)
This choice among suffixes seems to depend on the presence or absence of a non-adjacent morphological boundary, and as such, the phenomenon's status between derivation and inflection, between regular and irregular, will inevitably force morphological theories into some potentially uncomfortable positions.
Of course, some frameworks are simply not up to the task, straining to minimize its theoretical significance, or playing fast and loose with fragmented stipulations that cover the facts, but miss the generalization(s). Rather than crowning one framework as uniquely suited to the descriptive task, however, the very process of rotating through the lenses of diverse morphological frameworks presents a clearer, and indeed more coherent picture of the Sanskrit gerund than any single approach can.