If no, why not? And is it you physically/theoretically or practically cannot?
If yes, is this ever practical and does anyone do it? As I see it now, no matter what you are taking a fraction/subset of bitcoins entire hashing power so the difficulty of finding a nonce would take longer than 10 minutes to confirm.
As I see it, for this to be practical... Block reward + saved fees > mining costs * time
Where saved fees are the result of not having to pay other miners fees since you are doing it yourself and time is the time it takes to find the nonce. note: this miner wouldnt have to be running full time