David Ortiz - 7 times
No surprise here as Big Papi managed to pull the feat off seven times from 2004-2007 and 2014-2016. Ortiz put up some monster seasons including 2006 where he hit 54 homers and drove in 137 runs. For the better part of two decades, Papi was the class of the American League at the plate and rightfully did not have to wait very long to get into Cooperstown.
Jimmie Foxx - 5 times
Another unsurprising addition to the list as Jimmie Foxx is one of the best hitters to ever play the game. His five 35 homer, 100 RBI seasons came consecutively from 1936-1940, but they fail to tell the whole story about Foxx. See, Jimmie only played for Boston from 1936-1942 in the back half of his career. The first 11 seasons of his career were with the Philadelphia Athletics where he accomplished the same feat five additional times.
Manny Ramirez - 5 times
Oh, Manny. Younger Red Sox fans may not be able to fully appreciate how good Manny Ramirez was especially during his time with Boston. Much of that lack of appreciation is self-inflicted as Manny's legacy is tainted by repeated PED usage unfortunately. Ramirez joined Foxx with five 35/100 seasons in 2001 and from 2003-2006 and finished in the top 6 of MVP voting three times during that stretch.
Ted Williams - 4 times
Ted Williams is definitely a name one would expect to see on this list, but it is a little surprising to see that he only managed four 35/100 seasons given all of the other amazing numbers he put up. Williams accomplished the feat in 1941, 1942, 1946, ad 1949, but he also had six other seasons where he got one half of the requirement, but came up just short in the other category (in Williams' case it was usually in homers).
Jim Rice - 4 times
Next up, we have Jim Rice who was an absolute terror at the plate for the Red Sox int he 1970's and 1980's. The 1978 MVP winner reached the threshold four times (1977-1979 and 1983) in his 16 years with Boston and is widely considered to be one of the better players to ever wear a Red Sox uniform.
Mo Vaughn - 3 times
The days of Mo Vaughn hype were fun while they lasted. Few power hitters were feared more that Mo in his day and that fear was justified as Vaughn put up some gaudy offensive numbers when he was healthy. in 1995, 1996, and 1998, Vaughn also joined the 35/100 club with Boston before he moved on to the Angels and Mets and played a handful of seasons after that.