Ruth Davidson has called for more of the UK's political and cultural institutions to be spread around the country to create "a better Union".
The Scottish Conservative leader told a conference in London that "things will have to change" to maintain the UK.
First Minister Nicola Sturgeon is to publish a new paper to "restart" the independence debate later in the week.
Ms Davidson said making the UK less London-centric would help people "feel we have a real stake in it".
She suggested that a "newly-empowered fisheries industry" should be based in Peterhead post-Brexit, and floated the idea of a joint bid by football associations to host the World Cup across the UK.
Ms Sturgeon is to publish a new economic report on Friday aimed at beginning a new debate about Scottish independence.
This "growth commission", which the first minister first announced in September 2016, will look at what she calls the "economic opportunities of independence".
Speaking at a Policy Exchange conference on the Union in London, Ms Davidson urged supporters of the UK not to be "complacent", noting that "anywhere between 40 and 45%" of Scots back independence along with a majority of MSPs.
She said that "if we want the Union to flourish, indeed the UK to continue, then we need to work at it, to embrace change, and to think harder about how to do so".
The Scottish Conservative leader argued that Scotland and other parts of the UK "don't just need more devolution, they now need more Union too".
She said this could be achieved through "greater collaboration between our layers of government", and for cultural and political institutions to be shifted out of London.
Examples she cited included running the UK's fisheries industry from Peterhead, a "second home" for the British Museum outside of London, and a "joint UK-wide World Cup bid" - "as long as it doesn't mean a joint team on the pitch".
Ms Davidson added: "A country that spreads its power and culture networks across the country will ensure that all of us, no matter where we live, feel we have a real stake in it.
"Too many people feel that the Union is something projected onto them. Spreading its benefits around more evenly will ensure it is something they own; something they want to belong to."
In response, Ms Sturgeon accused the Conservatives of being "absolutely obsessed with Brexit".
She said: "It strikes me that what Ruth Davidson and the Tories' objection is, is not to a debate about the best constitutional future of Scotland - it's to a debate in which the positive independence case is heard."
Speaking before a meeting of her cabinet at the Clyde Gateway regeneration project in Glasgow, the first minister said the growth commission report due out on Friday would not "sugar-coat" potential "challenges" of independence, but would make an "optimistic, positive" case.
She said: "After a couple of years where the debate, not just in Scotland but across the UK, has been very much about how we limit the damage of Brexit, I think this a refreshing opportunity to have a debate based on hope and ambition and how we maximise Scotland's opportunities in future."
Ms Sturgeon said the timing of any future independence referendum was an issue for "later", referring back to previous comments where she said a decision would be taken once there was more "clarity" about the outcome of Brexit.
Scottish Labour meanwhile has argued that the SNP should focus on housing, economy and health instead of "igniting another divisive independence referendum campaign".