Usually, **yes if closing with EU LPs or using an EU vehicle**: the Cornerstone LPA should be treated as a **starting template**, not used unchanged.

Common areas needing local counsel review or amendment:
- **fund vehicle / governing law**
- **EU member-state securities offering rules**
- **tax**: withholding, VAT, treaty issues, carry treatment
- **AML / KYC, sanctions**
- **LP enforceability / default remedies**
- **side letters**, feeders, or parallel vehicles for country-specific needs

Rule of thumb:
- keep **core economics and governance** as standard as possible
- localize **regulatory, tax, and enforcement** provisions before closing

Reference:
- https://decilehub.com/base/1-general_questions/163972-cornerstone-lpa-how-should-the-cornerstone-lpa-be-adapted-when-a-fund-is-formed-or-operates-in-latin-america-rather-than-in-the-united-states-or-europe-which-provisions-normally-require-local-legal-review