It is permissible for a person to wear two layers of khufoof or socks. If he wipes over one – in cases where it is permissible to do so, as we shall see below – then he takes one off, and breaks his wudoo’, it is permissible for him to wipe over the other, according to the opinion of some of the scholars. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) a number of scenarios in which a person wears two layers of khufoof or socks, as follows: 

1 – If a person put on socks or khufoof then broke his wudoo’, then put on another pair before doing wudoo’, the ruling applies to the first layer, i.e., if he wants to wipe over them after that, he has to wipe over the first layer, and it is not permissible for him to wipe over the second layer. 

2 – If he puts on socks or khufoof, then he breaks his wudoo’ and wipes over them, then he puts on a second layer, then he may wipe over the second layer according to the sound view. It says in al-Furoo’: That is permissible according to Maalik. End quote. Al-Nawawi said: This is the best view, because he put them on in a state of purity (tahaarah), and their view that it is a lesser kind of purity is not acceptable. End quote. 

If we accept that, then the period of wiping starts from the first time he wiped over the first layer. 

In this case he may also wipe over the first layer, without a doubt. 

3 – If he puts khufoof on over khufoof or socks, and he wipes the outer layer then takes it off, can he wipe over the lower layer for the remainder of the period? I did not see any clear statement on this, but al-Nawawi stated that Abu’l-‘Abbaas ibn Surayj said that if he puts overshoes over the khufoof then one of three scenarios must apply: one of which is that they become like a single khuff, with the upper layer visible and the second layer like a lining, therefore he may wipe over the lower layer until the period for wiping ends from the time he wiped over the upper layer, which is like the case when the outer surface of the khuff becomes worn or scratched – it is permissible to wipe over the lining.” End quote from Fataawa al-Tahaarah, p. 192 

The “overshoe” (jurmooq) is something that is worn over the regular khufoof, especially in cold countries. 

Kashshaaf al-Qinaa’, 1/130 

Al-Sharh al-Mumti’, 1/211 

And Allaah knows best.