Blue Rush Watersports in Leverick has a dinghy you can rent. I just confirmed it can take 4 people. (let me know if you want their WhatsApp)
You can also try Bradley Powerboats. They used to have a dinghy but it maxed out at 3 adults (or 2 adults, 2 small children) I believe, but it looks like it was removed from her website for the 22/23 season. She does have a small powerboat if you are comfortable with that.
Both are very responsive and located right at the dock in Leverick.
You will love the Necker tour! Just make sure you confirm your reservation a week prior and make 100% certain you know your pickup location and details. Gumption's scheduling team is not the most organized or reliable bunch.