I looked at most doubles draws from recent years which was a quite interesting reading.
Most notable omissions are the Serra Zanetti
sisters who co-operated six times in '02 and '04, and the Rodionova's
who played together 3 times, including this year's AO.
All other unmentioned pairings in recent years got there via WC: Neha and Shikha Uberoi
(USO 2004), Evie and Daniella Dominikovic
(AO 2005), Carly and Chelsey Gullickson
(USO 2010), and most surprising, at least for me, Mallory and Lindsay Burdette
(USO 2006; Mallory was 15 and this was the first pro match she ever played at any level).
One pair of sisters who perhaps could have played a slam MD (both were inside top 100 in 2005, not sure what was the cut-off) but never did is Sandra and Daniela Klemenschits
As for the title question, I found a few with 3, but never more than that:
(a totally random find; 3 unknown pairs, two local and one American)
AO, RG, Wim, USO 2009
(Williams, Bondarenko, Radwanska)
RG, Wim 2010
(Williams, Bondarenko, Rodionova)
And of course the current USO 2012
technically had 4 pairs of sisters (Williams couldn't defend their title as Serena was injured) but only two of them - Bondarenko's and Gullicksons - played together, while the Radwanska's and Rodionova's teamed up with different partners.
Are you sure her sister even played competitive tennis? Never a slam, that's for sure.
Yes, just once, USO 1972. Chris was 17, Jeanne was 14.