AWS Api Gateway trigger multiple Lambda function

My current serverless implementation include
Client >> Api Gateway >> Lambda functions (Actual function returning data)
and these are about 50 + in numbers

While now we need to include tracking at each service call and modifying these lambda function is the last option i am looking for ,i am looking for architecture like any of below

a)Client >> Api gateway>>(Actual Lambda function & Tracking Lambda function)
b)Client >> Api gateway>>(Actual Lambda function & Any other API end point)
I am looking for stages “Method Request” or “Integration Request” in API Gateway from where if i could call any API.

Options for Tracking Lambda to be triggered by Cloud watch of Actual Lambda function can also be taken.
Please let me know if any other optimized way is present so the implementation can be done with least effort