Nobody has mentioned yet the missed approach height for imc rated approaches, these may well be above the actual cloudbase your flying around in.One thing I have had to do in the past is approach imc somewhere with an atc and half decent minimum approach height then skim in under the clag to get home.
You fly either VFR or IFR. There is no "halfway hacking it" option.
If you arrive IFR and go missed, then you have to fly the published missed approach.
If you got visual before DA/MDA why didn't you land?
If for whatever reason you went missed and doing so you are still (or again) in IMC then you have to either fly another approach (as published) or divert, as per the normal rules.
You do not go missed on an IFR approach and then duck down off the published missed approach procedure to get below cloud again, to fly somewhere visually!! The missed approach procedure is designed to avoid terrain and if you do "your own thing" off it you might well hit something.
One cannot do IFR ad hoc. One has to either fly VFR (that means being visual) or fly IFR (which means you may or may not be in IMC). The planning is quite different for the two.
There is no such thing as an "IMC rated approach". An approach is flown as published.