There was a time when consulting projects came in very specific shapes and only fit into the same-shaped hole.

If you had a strategy project you gave it to a strategy firm like McKinsey or BCG. If you wanted to outsource a load of your IT, you called Accenture, or maybe someone like Capgemini. If you had a financial management issue, you turned to the Big Four. Round peg, round hole. Square peg, square hole.

Digital transformation changed all that. The first thing it did was pick up the strategy and technology worlds and smash them together, until working out where one ended and the other began was almost impossible. Then it created demand for capabilities that no consulting firm really had—like the development of digital interfaces between organization and customer. Finally, it spilled over from the front office to the back office as the implications of all that customer-oriented work on the processes that sat behind them became clearer.

The result is that all of the world’s leading consulting firms are now hybrids—you can hammer most shapes of project into most types of firm without much difficulty. And that’s leveled the playing field, to the extent that the three firms who own the biggest share of the digital transformation market—Deloitte, Accenture and McKinsey—come from very different backgrounds.

For the advisory practices of the Big Four the good news is that the door to digital riches is open to anyone. But so far only Deloitte has managed to walk through it with any great success—securing itself a 12 percent share of the digital transformation market globally. There are probably two main, and very different, reasons for this. The first is ambition: Deloitte arguably spotted the opportunity first and went after it with greater gusto than its rivals, building up its own technology credentials, moving early to snap up a strategy firm in the shape of the beleaguered Monitor, and touting its end-to-end credentials. Its rivals were simply off the pace. Being the only firm not to have divested its consulting practice during the early part of the last decade probably helped, too.

But the other reason, arguably less commonly associated with Deloitte, was humility. Deloitte accepted its own limitations and set about building an eco-system of partnerships with smaller firms that did all the things—from digital design to 3D printing—it couldn’t. It even allowed Monitor to keep its name—offering strategy services under a Monitor Deloitte sub-brand, in recognition of the acquired firm’s strategy credentials and the absence of its own. In doing so it created a template—particularly where ecosystems were concerned—for others to follow.

And follow they did. The Big Four now spend as much time showing off the capabilities that exist within their ecosystems as they do talking about themselves, and although they’re some way behind Deloitte in terms of market share, all have built a platform from which they can, theoretically, start to challenge the leaders.

To some extent, the market appears to be moving in their favor: As the shift of the digital transformation story from front office to back office gathers pace, so the Big Four find themselves operating on increasingly familiar territory. Here, their operational and financial capabilities make a real difference, as does their ability to deliver complex projects that require scale.

But there are challenges, too. For a start, a recent survey of clients in the U.S. conducted by my firm, Source Global Research, has found evidence that everything that’s happened with digital transformation so far has been the warm-up act, in which clients have used digital technology to facilitate and accelerate existing priorities like cost-cutting or creating a better customer experience. The next phase, according to the survey, will be one that’s characterized by clients using digital to change not only how they do things, but what they do, and even who they are. It’ll be about more fundamental changes to business models, and what will matter more than anything else during this phase will be a consulting firm’s reputation at board level. The Big Four may have gone some way to furthering their cause in this respect through the acquisitions they’ve made—most notable of which was PwC’s acquisition of Booz & Co.—but more work is needed if they’re going to go toe to toe with the likes of McKinsey and BCG.

The bigger challenge, though, may come in the form of clients’ perceptions of their brands. Try as they might, the Big Four—and to some extent this includes Deloitte—struggle to shake off an image as accountants with a consulting division that’s singularly unhelpful when it comes to convincing clients that they’re culturally suited to digital transformation projects. Their existing customers might be more amenable to the idea, but our research suggests that their prospects still appear to need convincing.

In other words, what Big Four firms need more than anything else, if they’re going to win the digital transformation battle, is for people to stop thinking of them as Big Four firms.