'got something on' is correct and usable in written English.
You can use it to express that you are busy or have something to do. Example sentence: I can't go out tonight, I've got something on.
In fact, teacher Sara tends to use Modality to soften her many of her utterances, as in Example 7 (Table 6) below where she is avoiding questioning Cristiano too intrusively: Table 6 Example 7 1 SC What sort of house are you making, Cristiano? 2 Cn My one has got something on there.
You think you've got something on the sensor.
If you've got something on your mind, let it out.
"Maybe the Palestinians got something on paper and morally, but he got something on the ground," Mr. al-Qaq said.
"You've got something on your mind," she told me.
So when you've got something on your mind, tell it to me straight.
"I just wanted to say, 'Girlfriend, get something on!
They went around trying to get something on him.
"Folks were so consumed with getting something on the ballot for November," Mr. Newsom said.
"It's better to get something on record than nothing," he decided.
That workout was to get something on tape and to generate some buzz.
