Probably not I am afraid. Indeed, this label is a recently cooked up one, to replace an earlier one that used "Islamist" instead of "Muslim." The group claiming this apparently failing and declining label is the Ennadha Party of Tuinisia, founded in 1981 and still led by al-Ghannouchi, currently Tunis's Speaker of the House, although he and his party, which has led Tunisia for the last decade, may be about to be removed from power.
This is the 10th anniversary of the "Arab Spring," which began a decade ago in Tunisia, widely viewed as the one national "success story" of that pitiable affair. All the others: Egypt, Yemen, Libya, and others, ended up with dictators or endless war. Tunisia has a democracy! An informal economy merchant was hit up for bribes in the old regime of Ben Ali. He set himself on fire, setting off the whole Arab Spring.
In Tunisia it did lead to the fall of Ben Ali, with indeed a democratic government coming in, with the Ennhadha dominating as it has until now. They indeed espoused a position of "Islamist social democracy," and quietly ruled with near zero attention from most of the world for the last decade as Tunisia has just quietly stagnated over the last decade, no major uprisings, no terror attacks, just a lot of ongoing boredom. Problem solved. Move on.
As it is, I cannot explain why social democracy has not been achieved, Islamist, Muslim, or whatever, in Tunisia. I think the main reason is that the economy has stagnated. Tunisia has no oil or major industries. It has some tourism, although not big time, and some agriculture that gets exported to the EU, but it does not have a sufficiently highly educated populace to have any growing high tech industries. It has just been sort of plodding along, and with the current crisis, the failure of this regime to substantially improve the quality of life is coming home to pay.
It is highly likely that some sort of authoritarian regime will come to power in the near future, although probably not internationally troublesome enough to get much attention. But if this happens, it will be the end of the idea that the Arab Spring would bring about democratic regimes in the Arab world, which, with the possible now failed state example of Lebanona, does not exist seriously beyond Tunisia, the "success story of the Arab Spring," now unfortunately apparently failing on this decade anniversary of the uprising.