The first thing you must do is to decide whether the noun requires an article in the given sentence.
... people have become members
... things to do
... liquid on the floor
The idiomatic way to say "There are tasks which we must complete" is "We have things to do", without an article. If you wish to refer pointedly to those tasks, you could use the demonstrative ("We can't go to the movies. Don't you remember that we have those things to do?"). Or if you wish to make those specific tasks the subject of a sentence: "The things we have to do are not easy to do".
Then you have to ask whether the quantifier allows an article. Some do, some don't.
A plenty is ungrammatical when used in a partitive sense.
Plenty of the liquid is on the floor, even though most of it went down the drain.
"Plenty" works just like "some" or "much"
Much of the liquid is on the floor.
A much of ... ungrammatical
Some of the liquid is on the floor.
A some of ... ungrammatical
But we can say "a little" and "a few".
A little of the liquid is on the floor. The little that did not
spill remains in the bottle.
Little of the liquid remains in the bottle.
A few people remained on the train platform when the announcement was made that the train had been cancelled. The few who remained did not believe the announcement, and they were correct.
Few people think SEPTA is well-managed.