Books: There is no limit on what you can request through I-Share (double-check that), nor is there a limit on how many books you can request through the national consortium.
Journal articles: There is no limit on how many articles you can request through Interlibrary Loan. However, there is a limit on how many recent articles you can request from a single journal. Under U.S. copyright law,
A borrowing library may receive copies of up to five articles from a single periodical title each year without paying any copyright fees. For each copy beyond that, a license fee (or a subscription) is required. This rule applies only to articles published within five years prior to the date of the ILL request. (“Modern Interlibrary Loan Practices: Moving beyond the CONTU Guidelines,” ARL White Paper, August 31, 2020)
This is known as “the rule of 5.” Once a library has exceeded this limit of 5 articles, the patron must pay for the article. (Right now, we do not offer the service of purchasing the article for the patron; they can order it from the journal’s website. Patrons may also petition the university to subscribe, or travel to a library that subscribes to a paper version of the journal and consult it.)