In A more general abc conjecture, p. 7 Paul Vojta conjectures exponent $1 + \epsilon$ outside a proper Zariski-closed subset
Your question appears in The abc-conjecture and the n-conjecture,Coen Ramaekers p. 23
5.1 Strong $n$-conjecture. Adding pairwise coprimality, the exponent is $1$ without additional restrictions. Searching the web for it returns only 3 hits.