Yes, you can do a PIA with positive equity.
The PIA should be successful if they can demonstrate that the loan could be paid in full by the time they are, say, 70 years old.
A PIA could also be successful (but would be more challenging) if they agreed to continue paying interest and some capital, and then "trade down" at 70 years and pay off the residual debt at that time etc.
A consideration is what court is going to hear any re-possession proceedings. Some courts might resist making a re-possession order given that full interest and some capital is being paid.
Jim Stafford