It appears my Lewis line are others related in RI are descended from the Maxsons at least 4 times. Here's how:
1. -- Daniel Lewis Sr. m. Mary Maxson, 1701 in Westerly RI. This is Mary, the daughter of John Maxson Sr. and Mary Mosher. -- Daniel Lewis Jr. m. Martha Prosser, in RI. -- Elias Lewis Sr., b. 1730, Westerly, RI., m. Susannah Reynolds, 1749, Westerly, RI -- Eunice Nancy Lewis, b. 1753, Hopkinton RI, m. Thomas Smith III, 1782, in Hopkinton (It is Eunice and any of her siblings who will have at least 4 Maxson lines)
2. -- John Maxson Sr. and Mary Mosher -- John Maxson Jr., b. 1666, Westerly, RI, m. Judith Clarke -- Susannah Maxson m. Zacheus Reynolds -- Susannah Reynolds m. Elias Lewis Sr., 1749, Westerly -- Eunice and siblings.
3 and 4 It seems that Mary Mosher was Maxson descendant too, meaning that each line above is already a double Maxson line. Mary Mosher's mother was Lydia Maxson. This is with the caveat that there is dissension about who Mary's father was, Hugh or Nicholas. She did have a brother named Hugh who married one of John Maxson Sr.'s sisters. It is not known what relation Lydia Maxson was to Richard Maxson, the father of John Maxson Sr.
Would appreciate any additional information on these and other lines. Didn't know I even had any relatives in New England until a few months ago. I now have found distinct lines in both of my grandfathers' seemingly unrelated families (one in KY, one in PA) that go back to Westerly, RI in the 1600s. The KY line descends from Eunice Nancy Lewis Smith. The PA line includes Satterlee, Coon/Maccoone, Lamphere/Lanpheare, Preston, and Hulet. I'd wouldn't be surprised to find more Maxsons in either line.