The Imām said, “I want to remind some of our brothers present here that when they came in they would give salām to every person sitting down individually or to a lot of them, so when they would shake hands they would say, ‘As-salāmu alaikum, as-salāmu alaikum …’ and so on. What I wanted to remind you of, and reminders benefit the believers, is that when someone comes to a gathering the sunnah is for him to give salām in general to all present, saying, ‘As-salāmu alaikum wa raḥmatullāh,’ and if he is able to shake everyone’s hand individually, then without doubt that is more perfect a thing for him to do and more complete, and if he can’t, because there are too many people, then in such a case it’s enough for him to give salām [in general to all].
If he were to follow up on his salām by shaking everyone’s hands then it is not part of the sunnah whatsoever for him to [then go and say] say, ‘As-salāmu alaikum, as-salāmu alaikum, as-salāmu alaikum …’—this is an innovation [bidʿah] of this era which the past generations never knew, and I’m not saying just the Salafī generations but rather the Salafī and the Khalafī [the generations who came after the first three] ones. This kind of handshaking was not known except in this present generation.
And this is a reminder and reminders benefit the believers, this was something [I wanted to say] before any questions you might have …”
Silsilatul-Hudā wan-Nūr, no. 0836.