Why my mesh gets distorted when adding multiple support loops and mean creases?

I have a smooth mesh with minimum subdivision loop cuts. I’m adding multiple support loops where the mesh makes a dent in it and also moving some vertices around and added mean crease all the way up to one. I don’t want to add loop cuts in the middle or it will deform the model. besides the model becoming messy, when I apply the subdivision modifier, the corners start to protrude. How can I fix this?

Well you have to support the corners. Crease them or add a edge. If you crease just the part of the edge as you did then the bad artifacts are made. You have to crease whole edge or at least to the point where is no curvature so it will look ok. Better to support this with some added geometry. Also if I see correctly you have Ngons in your mesh.

Here’s a closer screenshot of my topology. The mere problem adding edge would mean that the rest of the mesh would distort. are these support loops what you had in mind?