DNA Match - Double distant Cousins?

Finding relatives through DNA consists of looking at and evaluating the DNA match and then working through the genealogy paper trail to find out when and how we are related.  Two sisters, Joy and Lois, contacted me about a match.

Ancestry.com and GEDmatch,com calculates that Joy and I are 4th cousins which would mean that we share our 3rd great-grandparents.  FamilyTreeDNA calculates that we are 2nd - 4th cousins meaning that we share our great-grandparents, our great-great-grandparents, or our 3rd great-grandparents.  Based on the paper trail we have figured out that the closest common ancestor would be our 3rd great-grandparents.

Joy, Lois, and I started digging through the family tree looking at names, places our ancestors lived, and dates.  We came up with what we think is a pretty solid match - the Duggan family in Abbeyfeale, County Limerick, Ireland.  We don't know the names of our 3rd great-grandparents but we believe that my Hanora Duggan and Joy and  Lois's Thomas Duggan are siblings.  And this would be the end of our search for a straight Autosomal DNA match.  But we have an X-Match and my Hanora Duggan can not have passed down an X Chromosome to me!

Women have 2 X Chromosomes and men only have one that they received from their mother. So no X passes down on a man's paternal line.  The passing of an X Chromosome is difficult to conceptualize using normal genealogy charting.  Blaine Bettinger designed a white, pink, and blue Ancestor Fan Chart that has become the standard in visualizing X inheritance.

The white blocks do not pass an X chromosome to the center person in the chart who is my Dad in this diagram.  Hanora Duggan is on the white side of this chart.  So that means Joy and Lois and I have another common ancestor on the pink and blue blocks. But almost all my 3rd great grandparents in the pink and blue blocks are blank - I don't know who they are.

Duggan is an X line for Joy and Lois, so somehow, somewhere the Duggans and at least one of my nameless 3rd great-grandparents in pink or blue are related.  Based on location, Edward Maloney's mother is the most likely candidate, but since I don't know Annie's last name or where in Ireland she was from, her parents are also possibilities.  Anne Joyce is from Mayo so her mother is not a likely candidate.

"Double cousins" are usually cousins who share both sets of grandparents instead of the usual one set.  This happens when 2 siblings marry into the same family. So we don't fit the normal definition, but this extra connection we have means we are doubling up on the DNA connection somewhere.