as salam alaikum
Salat differs from voluntary invocations and supplications. The intention during Salat is to pray for Allah only. However the recitation of Sura al-Fatihah is mandatory wherein it is said "Guide us to the Straight Path" (1:5) which in itself is a prayer for ourselves and others as well.
It is also possible to pray for others during the qunut.
With prayers for your success.