Is it possible to allow students unlimited number of attempts?
I want to set 'pass grade' to 4 of 5 points, but at the same time I want to allow them to make additional attempts even if they have already reached 4 points.
You're talking about Quiz.
I'm asking about Assignment.
Then just set 'attempts reopened' to 'manually', instead of 'automatically until pass', then you can allow an extra attempt each time the attempt is graded.
Yes, that's what I do.
But I want to allow students to send another attempt even before I graded the previous one and manually reopened it. Sometimes they catch and fix mistakes themself

By the way, if I set 'allow attempts' to 'manually', how can I set default value of 'allow another attempt' to Yes on the grading screen?