I wanted more a discussion about what can be called a variant, and variant of what, but it looks more like the standardists/prescriptivists are going to swamp this thread with their view of correct grammar. It's not really for me to have to defend a certain dialectal use. Ah, well.
Onward:
2.4 Modal stacking
The complement of a modal cannot be a Finite verb, as there is no room in INFL for a second instance of Finite/Deixis. This explains why standard English, which has no nonfinite forms of modals in its lexicon, does not allow modals to be "stacked" as in (40b).
However, German and some non-standard dialects of English do allow stacking. Within the framework presented here, the simplest way to account for modal stacking is to say that languages that permit stacking have infinitive forms of modals. In German, infinitive forms of modals bear the usual infinitive suffix -en, as in (40b).
In stacking dialects of English, the
infinitive forms of modals are generally phonologically identical with the present or past finite forms. For example, in the sentences in (43) (taken from Di Paolo 1989: 195), can, should, and oughta function as infinitives.
(43) a. We might can go up there next Saturday.
b. This thing here I might should turn over to Ann.
c. Well, once we get under way, it shouldn't oughta take us very long.
Since the present and past forms of English modals have been diverging in their lexical semantics, it is not entirely surprising to observe that they are treated as uninflected forms of separate verbs in some dialects.
http://www.chass.utoronto.ca/~danhall/hall.generals.2001.pdf
Grammar at work (conscious restriction):
"while the full range of stacked modal constructions attested in English dialects and
English-based creoles is wide,
each individual dialect permits only a restricted subset of
combinations of modals."