Jetway12345
If you hold an FAA Commercial Single Engine license you dont need to give the tech specific exam even though are giving the skill test in India .
Multi on the other is a little different since it says on the flow chart pass result of tech specific exam .
From the Flow chart
NOTE 2: For Multi endorsement on CPL:
1. Record of ground training and pass result of technical exam
2. Statement indicating at least 10 hrs of training on multi engine aircraft for which endorsement is requested (including test/ check),
You can ask the flight school where you do the recency and skill test for the multi to conduct a tech specific exam . You also need ground class vertificate saying you underwent atleast 20 hours of ground training on the specific multi engine aircraft