Once internal vs. external inflection came up on ADS-L (originally with respect to double downed instead of doubled down; discussion here), people began looking at other interesting cases of inflection in composite expressions, including in the odd verb re-up ‘re-enlist’. Wilson Gray reminisced about his army days, reporting
the conflict in the barracks, back in the day, between the supporters of re-ing up and the backers of re-upping.
Naturally, each side thought that the other side was seriously compromised in its control of derivation in English.
There’s no question that, historically, re-up has the derivational prefix re- ’again’ in combination with something functioning as a V (since the whole thing is a V), so that inflection would fall on the second, head, element (re-upping). But up also often functions as a Prt, so that an alternative analysis of re-up would treat it as composed of a mystery V re and the Prt up (predicting re-ing up), instead of as a prefix re- with a mystery V up (distinct from the V up ‘increase’ in up the price, up the ante, etc.).
The historical evidence seems to clearly point to re- + a V up as the original, and indeed OED3 (March 2010) lists re-up under its main entry for the V up. So re-upping, re-upped, and re-ups are the older forms (the only ones in OED3′s citations) and they seem to still predominate for the ‘enlist’ verb, though for many people the inflections have been “internalized” (at least variably).
[A side issue: the etymology of re-up 'enlist'. OED3 has the up as a V
with reference to the holding up of one's right hand on taking the oath of enlistment into the United States armed forces
Several ADS-Lers found this proposal preposterous, since the oath-taking ceremony plays little role in re-enlistment, instead suggesting, reasonably, that the up was a shortening of sign up. At first, I entertained the possibility that the OED's etymology was correct as to first uses, but that people had quickly reinterpreted the relationship of the parts of the verb. So I looked back at the OED's citations:
1. intr. Services' slang. To re-enlist in the armed forces.
1906 Soldier Slang in C. M'Govern Sarjint Larry an' Frinds App., Re-up, to re-enlist.
1913 Army & Navy Jrnl. Philippines 4 Oct. 15/1, I had to go or else re-up For seven long years hitch.
1942 E. Colby Army Talk 174 When enlisting and being sworn in, a man is said to ‘hold up his right hand’ for three years. So when he does it after being discharged, he ‘re-ups’. [further cites follow, with extended uses, both transitive and intransitive, from 1921]
Ah, the 1942 cite is the crucial one, and it looks like a post-hoc rationalization of the expression in terms of the swearing-in ceremony — a nice story, but no more than that (especially 36 years after the first appearance in print).]
Now for another layer of complexity. There are other senses of re-up (or re up), having to do with drug use. From Green’s Dictionary of Slang, following the ‘re-enlist’ sense:
2 (U.S. drugs) to replenish one’s stocks of a drug. [cites from 1975 on; all cites in BSE or in PRS=BSE]
3 (U.S. drugs) to take another dose of a drug. [cites from 1995 and 1997; both in BSE]
From these cites, we learn nothing about the location of inflection for these uses, since none of them have visible inflection on the verb. But there are plenty of examples of re-ing (or re’ing) up, re’d up, and re’s up in the drug sense from rap/hiphop, as in “Roc Boys” by Re-Up Gang (with reference to cocaine use):
Show money, blow money, the Re-Up Gang agenda
You niggers re-ing up with them low ass dinners (link)
There’s even a nice use in a metaphorical sense, with love treated as a drug, in “All” by Olivia:
O’ding over you but still I’m re’ing up (link)
Internal inflection seems to be gaining, especially for black speakers.