Hi there,
I shoot a lot of close-up images. First and foremost, depth of field can be checked via stopping down before the shot is taken. Most advanced cameras have a stop down option. So, I use that feature when I want to decide between various depth of field settings. Although after about fifty years behind the lens I can decide on my setting without too much checking.
Now, if you are really serious about close-up and macro photography then a good carbon fibre tripod is your best friend. Then you can take photographs with different aperture settings in A priority and pick your most desirable shot in PP.
If you are even more serious about close-ups then you even may consider getting into stacked frames photography. Either with a macro rail manually or via a StackShot rail and Zerene or Helicon Focus. Stacking frames can give you the best quality for achieving either an extended depth of field or the best section of plain of sharpness.
Hand holding for close-ups works well with today's high ISO capable cameras but taking photos of identically framed subjects while you change aperture only work from a tripod. Even if there would be a camera setting that would allow changing aperture settings while retaining exposure values in a bracketing mode would not be totally satisfactory. When you shoot close-up and macro then minute changes in body posture can cause discrepancies in framing.
I whole heartedly suggest to shoot close-upimages from a tripod. I have several tripods. My choice for close-up images with a 100mm macro and up to 300mm with auxiliary attachments is a No. 2 size tripod. It does not have to be a Gitzo just any good carbon fibre tripod that has similar ratings as a Gitzo No. 2. I use a relatively inexpensive Benro 2580 with a good ball head. On occasions I use a macro rail on this tripod, an old Nikon rail that I modified to accept Arca-Swiss plates for quick setup.
What you need for convenient tripod work is a tripod that is easy to operate, supports your gear without vibrations, can be set up for low low to the ground use. Once you develop a habit for using a tripod when shooting close-ups you never will look back. Your keeper rate will shoot high up and you will wonder why you didn't shoot from a tripod before. It is easy, it is only a small adjustment in mindset.
Best to your close-up ventures, AIK