The questioner says: He put on a second pair of socks after wiping over the first pair, is he now allowed to wipe over the second pair?
There is no problem with that (i.e. wiping over a second pair in this case), as he is still considered to be wearing khuffs. But the period for wiping over the socks runs according to the first pair, i.e. it starts from when he first wiped over the first pair.
Shaykh Muhammad ibn Hizaam – may Allaah preserve him
Abu Yusuf Abdulfattaah