So, Mayhoola for Investments — the Qatari sovereign wealth fund that owns Valentino, Anya Hindmarch and Pal Zileri, and that is backed by Qatar’s royal family — has bought Balmain, the Paris fashion house backed by the Kardashians (well, not exactly backed, but they are its biggest cheerleaders). This could have big repercussions on what we all wear.  Since 2005, when the designer Christophe Decarnin transformed the couture house to haute rock ’n’ roll hotness, Balmain has been a brand whose buzz — with its own name, “Balmainia” — is significantly bigger than its bite of the market.  Mr. Decarnin left in 2011 (reportedly because of stress), after convincing numerous women that they really, really desired a pair of wildly expensive crystal-bedecked ripped jeans. Olivier Rousteing, then 24, took the reins, altering the balance between glitz and grunge in favor of the former.  Mr. Rousteing’s Instagram account has 3.4 million followers, Balmain has 4.7 million (both of which pale in comparison to Gucci’s 9.1 million, though no one really seems to care). You’d think, by all the hoo-ha around his account, that Balmain would be a megamaison.  But if reports of its sales (around 130 million euros, or about $135 million, in 2015) are correct, it’s more in the lower-middling range, and very reliant on the marketability and profile of its young designer. Mayhoola is betting that it can get larger.  Part of Mayhoola’s assumption is probably that Balmain’s growth has been held back by the death in 2014 of Alain Hivelin, the owner and the greatest booster of its reinvention, and by the fact the house has been owned since then by a family-owned holding company that did not seem particularly impassioned about fashion.  That may be true. But the gap between image and sales may also be a result of the fact that Balmain is somewhat of a niche taste, marked primarily by an unabashed 1980s “ynasty”-meets-Vegas-high-roller aesthetic.  Elaborately and expertly made though it may be, it still has very specific appeal. Kim Kardashian and Kanye West love it. So do many models: It was one of the most-worn brands at the Metropolitan Museum of Art Costume Institute Gala this year.  But a giant social media/reality TV following does not necessarily a giant consumer base make (it’s unclear how many of those vicariously living Mr. Rousteing’s life are actually able to buy his clothes). To become a major player, Mr. Rousteing has to extend his aesthetic.  His collaboration with H&M in the fall suggests he understands this, though the pieces were essentially just less-expensive versions of his greater hits; they let wannabes into his world, but they didn’t expand it.  More interesting, really, were a few garments hidden among the otherwise over-the-top hourglass excess and boudoir trousers in his last collection: a peach-colored cashmere wrap coat, a dove-gray suede dress with a bit of safari lacing.  They suggest formerly hidden depths of subtlety in Mr. Rousteing’s creative arsenal, and the possibility that more refined layers could, indeed, be built into the collection that would appeal to a wider group of women, much in the way Dolce & Gabbana may promote an image of lusty Italian corseted mamas, but sell a whole lot of terrifically cut pinstriped suits.  By all accounts, Mayhoola has been a good partner for Valentino, investing in that brand — remember the blowout couture show and store-opening celebration the house had in Rome last year? — helping take it to the billion-dollar level, and grooming it for a rumored initial public offering. (Fashion loves an I.P.O. rumor.)  If the fund can do the same for Balmain, the house could be transformed once again, this time into a major presence not just in the digital and celebrity worlds but also in the real world. But it can’t happen without Mr. Rousteing buying into a broader agenda.  He’s having his men’s show on Saturday, too soon to see any effects from the new owners. But by the time Paris women’s wear is shown in late September, it will be a different story. Whether it will be told on the runway remains to be seen.
Maybe Mayhoola for Investments, the Qatari fund, will help move Instagram’s favorite fashion brand beyond the Kardashian clan.