Can you suggest a list of reputable, invitation-only dating platforms?

Yes. If by invitation-only you mean platforms that use applications, screening, referrals, or a waitlist rather than letting anyone immediately create a dating profile, these are worth looking at:

• Raya — One of the best-known private dating communities. You apply and enter a queue; applications are reviewed before acceptance. It also includes networking and friendship alongside dating.Raya+1
• The League — Uses an application/waitlist system and describes its community as curated. It emphasizes education, career ambition, authentication, and relatively selective daily matches.The League+2
• Inner Circle — Applicants are reviewed by a membership team, and not everyone is accepted. The service focuses particularly on lifestyle, interests, and an active social community, including events.Inner Circle - Curated Dating App+2
• Luxy — A selective dating platform with profile review and identity/verification procedures. It is particularly oriented toward affluent/high-income dating, so its positioning is somewhat different from Raya or The League.Luxy+2

At a glance

One important distinction: “invitation-only” isn't always literally invitation-only. Several of these now allow prospective members to apply directly, while retaining screening or approval mechanisms. For example, Raya accepts applications into a review queue, and Inner Circle explicitly says each application is reviewed and that some applicants aren't accepted.Raya+1

If you're looking specifically for high-net-worth/elite, professional/executive, celebrities/creatives, or serious relationship-oriented platforms, I can narrow the list accordingly.