I am trying to have a rectangle extrude from a cylinder. I can get that working fine, but as soon as I add a subdivision surface I get smoothing that creatives overlapping vertices. I don't know a strategy to solve this and I'm hoping someone will help. Please see the images. I have tried increasing density but I still get the problem at the corners. I have added edge loops to the bevel, which kind of works, but you can see that the horizontal loops are still bending around the cube extrusion and it causes some lighting issues. Does anyone have any tips on what I could do to prevent this? Thanks for any help.
Image 1: The object I'm trying to smooth.
Image 2: The result of adding a subdivision surface. Note the shading problems at the corner.
Image 3: The result of applying the subdivision surface. You can see that it's rounding the cylinder and in doing so folds / overlaps vertices from the corner.
Image 4: Increasing loops for bevel. Still warping the cylinder causing shading issues.