I'm guessing "parent plus" is a SL. Moving it here for more help.
I believe that Parent Plus loans DO involve some form of credit check, but I'm not positive on that. If they do, it's possible you could be denied because of the state of your credit and debt-to-income ratio. I would call the financial aid office at your child's school and ask them what the process is for getting a Plus Loan (does it involve a credit check) and what the guidelines are.
PLUS loans are credit based. You will more than likely be denied. However, you child will then be entitled to additional unsub loans.
From the DOE site
If a dependent student's parents are denied a PLUS loan, or the college
financial aid administrator determines that the parents are likely to be denied
a PLUS loan, the student becomes eligible for increased unsubsidized Stafford
Loan limits, the same limits as are available to independent students
Yes, you can be denied. Before my credit improved, I would apply every year to get denied then they would give my son an additional $4,000.