Shaikh al-Albanee said:
From among the widespread innovations of this time… is that one gives salām to everyone he shakes hands with.
So he says:
“salāmu ʿalaykum, salāmu ʿalaykum, salāmu ʿalaykum”.
If there are twenty people in the gathering he gives twenty salāms; this is an innovation.
Rather, the Sunnah is that when a person enters upon a gathering that he say:
“salāmu ʿalaykum” once…
Source: Silsilat al-Hudā wa-al-Nūr (#181)