The phrase "limited exceptions" means there are only a few specific situations where something is allowed or given special treatment, while the general rule remains different. Full definition
The plant is scheduled to operate on a daily basis with limited exceptions for high winds or unforeseen events. (guntherportfolio.com)
Nobody has time for an epic - length resume, and with very limited exceptions there is no reason for your resume to exceed a couple pages. (grammarchicblog.com)
That's based on roughly 150,000 students tested per grade, with limited exceptions for students with severe disabilities. (chicagotribune.com)