While answering another question about maybe, I was reminded of the existence of a specific pattern of expression. Here are a few examples from the Corpus of Contemporary American English:
"For Israeli-Born Chef, Hummus and Tehina are a Bridge to Home." Fresh Air (radio program), 5 May 2017.
So it's natural to go out, to maybe have a couple of drinks and wind down.
"Coverage of 89th Academy Awards," CNN (news program), 27 February 2017.
They will come in here, maybe have a little libation, have some food courtesy of Wolfgang Puck, maybe have some chocolate as well, and party, right.
Steven Hayward, To dance the beginning of the world : stories. 2016.
When he left the service he came back to the Springs where he planned to open a practice, get married, maybe have a couple of kids.
Literally describing the usage poses little problem. "Maybe" functions as an adverb that qualifies the verb phrase it is proximal to. In a list of verb phrases, maybe adds a candid quality. It has temporal logic, where the more definite item often comes first and is followed by a more uncertain or optional activity. It feels glib and colloquial. I'll write this question, put it out there, maybe get some answers.
However, I have no idea when this specific application of maybe as a glib conjecture became commonplace.