Joe Andrew is global chairman of Dentons, the world's largest law firm. As architect of the firm's strategy, he has overseen a series of international mergers, most notably last year's combination with Chinese law firm, Dacheng. Asked to serve by President Bill Clinton, Andrew became national chairman of the Democratic National Committee from 1999 to 2001. Since joining Dentons as a corporate lawyer in 2004, he has advised on deals worth more than $500bn, most notably in the healthcare and insurance sectors.

Dentons is different in many ways from other law firms. It dares to innovate even in leadership. "Of all the big global law firms, we're the one which has two leaders at the top," says Andrew. In referring to Elliot Portnoy, global chief executive officer (CEO) of Dentons, he adds: "Elliot and I are literally tied at the hip. We have different areas of concentration in the process as well; we do virtually everything together and there's nothing that I do that Elliot couldn't do, or isn't involved in in some way in the process."

Andrew sees Dentons' leadership structure as a metaphor for the firm: "We have team leadership throughout the entire process and we've done an effective job of making sure that power is as close to the decision makers who actually understand the particular details in each given area.

"We call that polycentric. That is our principal innovation. It is often misunderstood because polycentric for us is not just marketing, how we go to market, it's how we've organised the entire firm. It's what allows us to be able to have decision making as close as possible to the stacks on the ground, which allow us to be able to make the best decisions in the process and therefore have this multi-headed strategy all operating at the same time in the same place."

Andrew never stops innovating: there are many feathers in his cap. Given the scale of his responsibilities – "we have more than 7,500 lawyers in 144 locations in 58 countries around the world, with people who speak 72 languages" – he certainly needs to. The firm's most recent high profile innovation, Nextlaw Labs, is one such innovation.

Its purpose is to help resolve a conflict between two competing objectives, as he explains: "All law firms, particularly large firms, are faced with a challenge: our clients want us to use new technology and new processing to increase quality and reduce cost. At the same time, they only want to hire lawyers who have the right level of experience."

As a solution, he describes Nextlaw Labs as "a skunk works" – a term borrowed from IBM – "where the things that might not be perceived today to be core to your business but you believe will be later, are done in a separate entity". He adds: "The idea is that you can bring people together to collaborate in a place that is not internal to the law firm itself."

Nextlaw Labs was founded because "as technologies develop at different rates, we don't know which technology will be the winner", says Andrew. It aims to do four different things: "It can evaluate new technology that comes up; it can invest in those technologies so that we reap the benefit of trying to be involved in them; it enables us to develop our own technology; and it helps us take existing technology and form a suite of services."

Nextlaw is conceived as a brand for multiple entities, each of them centred on innovation. There are seven, as yet unannounced, ideas in the pipeline. Apart from Nextlaw Labs, the other one that has seen the light of day created significant waves and generated publicity across the legal world.

If you think about the Uberisation of law, that is what the Nextlaw Global Referral Network allows us to do

In May, Dentons launched Nextlaw Global Referral Network (NLGRN), which allows independent firms to collaborate at no cost. "If you think about the Uberisation of law, that is what NLGRN allows us to do. Fundamentally, what it does is to match clients out there to the specific talent that they need."

Andrew outlines the strategy: "We're the world's largest law firm, but we're honest that we're not the best law firm for each client in each given place," he says. "There are many places in the world that we are not in at all – more than 300 cities with more than a million people in them that we are not even in – and we are far bigger than anyone else. If you're honest about truly having a law firm that has global reach, you have to see other law firms not as competitors, but as collaborators."

The challenge with existing law firm networks, he suggests, is: "They're all pay-to-play: the only way that a network can work and still have an executive director, a website and somebody who answers the telephone, is that you've got to pay a fee. If you pay a fee, you tend to want to exclude competition."

Andrew explains that the goal of NLGRN is "to use a technology platform, which makes it less expensive, delivers a better service and is more accessible, and simply say: we will pay for any other cost and so the network can actually be free". He continues: "The only qualification to be in the network is the quality of the firm and no one has to pay. Why does our referral network succeed where others don't? It's because there's no barrier to entry, it's free and it's not territorially exclusive. World's largest law firm plus world's largest referral network – that's the future of the legal profession."

How well has it worked so far? "We have the problem of success," Andrew says. "We have significantly more law firms seeking to apply, particularly firms that we do not have a pre-existing relationship with, that have to be vetted by the committee. So yes, we are on schedule, everything is working out well, but we are honest to say we are a bit overwhelmed by the response.

"Think of all the great law firms that are out there that may have five or 10 lawyers; 95% of the legal profession is with people in law firms of less than 100 people. No one would let them in to a referral network. Now, all of a sudden, they're saying: 'I can be in a referral network with the world's largest law firm'."

Andrew has a vision: "To be able to look in the eye the most sophisticated multinational corporation in the world, which is going to give out high value work, and say: we either have, or I can instantaneously find for you here on my smartphone in my pocket, the exact right lawyer, in the exact right location, in order to handle your challenge. We've identified what we consider to be 263 unique jurisdictions, which we think are key, right now, based on GDP and analysis of legal work, that we need to have either one very good law firm or multiple law firms in."

In September, Dentons announced that Stephen Harper, the former Prime Minister of Canada from 2006 to 2015, had affiliated with the firm. Another coup for Dentons and another feather in Andrew's cap.