Adiyen observes vratam on Saturdays for Thiruvenkatamudaiyan not for any benefit but out of affection. Adiyen partakes of fruits, milk, or any wheat-based food on Saturdays. Can those who have undergone bharanyasam observe these vratam-s? If Dwadasi occurs on Saturday how to conclude Ekadasi vratam?

There is no need to observe any other vratam apart from ordained vratams like Ekadasi, Sri Jayanthi, and Sravana Dwadasi for those who have done bharanyasam; but it is not wrong to observe vratam for Thiruvenkatamudaiyan.
Those who observe vratam on Saturdays should observe Dwadasi paranai in the morning and fast during the evenings; if Dwadasi occurs on Saturday, Dwadasi takes precedence.