Is there anything we can add to the present Euclidean Geometry? I did not study the detail history of Euclid. As far as I know, the geometry starts from a few postulates and keeps on expanding (through theorems developing) to the present state. Even with these theorems as tools, proving some facts (in some geometrical problems) still is very clumsy. I am thinking “Is there anything we can include in it” to makes it ‘stronger’ so that proofs becomes easier.
Let me give a simple example (and I hope I am correct). In my school days, we were using Durell’s book. In which, the ideas of “transformations” were never taught. Thus, adding them to the Euclidean geometry makes it ‘stronger’.
Restrictions:- (1) by geometry, I mean plane geometry; (2) "Euclidean geometry" has been used as keyword to search through SE, and re-direction to this site may not be necessary.
 A: First, the idea of "transformations" is not something that was added to Euclidean geometry; rather, the concept of Euclidean geometry as the study of invariants of Euclidean space under affine transformations is simply a more modern take on the five axioms.
There are certainly studies of the underlying axiomatic system of Euclidean geometry, in fact it is quite famously the oldest axiomatic system that endured scrutiny throughout mathematical history. Modern takes on this are a bit of an ongoing topic of research; Hilbert, Tarski, and Birkhoff each came up with their own axiomatic systems to describe Euclidean geometry. It would really fall under the category of logic/set theory rather than geometry though. If you are interested in what theorems of Euclidean geometry depend on which axioms, and how strengthening/weakening the axioms affects the theory, you should check out this line of thought.
For a possibly relevant (though not duplicate) question, check out Research in plane geometry or euclidean geometry.
