Benefit: The Innovation of Greeting People One-by-One When Entering a Gathering
In the Name of Allāh, the Ever Merciful, the Bestower of Mercy
Rather, the Sunnah is that when a person enters upon a gathering that he say, “salāmu ʿʿalaykum” once, after this if it is possible for him to shake hands with those present in the gathering then that is better. If it is not possible for him to shake hands, he has accomplished the obligation of the Muslim giving salām to another Muslim—one fifth (of the rights a Muslim has upon a Muslim)—that if you come upon another Muslim, you give him salām. As for shaking hands, this is a recommended Sunnāh.
Like some of the companions have said:
We have not come upon the Messenger of Allāh (صلى الله عليه وسلم) except that we shook his hand.
So adding to the Sunnah al-Qawliyyah (the Prophet’s speech) or Sunnah al-Fiʿliyyah (the Prophet’s actions) is an innovation in its essence. For this reason, if it is said that adding good [to the sunnah] is good, [it is said] this speech will not save you because if it was truly good we would have been preceded in it (by the early generations). This is my advice.
Source: Silsilat al-Hudā wa-al-Nūr #181
Translated by: Munīb al-Ṣumālī