The party's enterprise spokesman Murdo Fraser will argue the radical restructuring could unite Unionists and many nationalists if independence is rejected in September's referendum.
Mr Fraser, who lost the party's leadership contest to Ruth Davidson in 2011, will use a lecture at Glasgow University to outline a vision of the UK as a patchwork of administrations in Scotland, Wales, Northern Ireland and the English regions.
Under his plans, the present devolved authorities plus new administrative areas of England would all enjoy similar powers, including wide-ranging control over taxation.
The UK would be governed at federal level by a substantially reduced House of Commons, while a US-style Senate, with equal representation for the UK's autonomous nations and regions, would replace the House of Lords.
The new arrangement would be laid down in law in a written constitution.
The Mid Scotland and Fife MSP, will set out his ideas in the first of lecture series, Visions of Scotland, organised by think tank Reform Scotland and the university.
He will admit that English regional autonomy - which was rejected by voters a decade ago - is a "thorny problem" but suggest the North would be more willing now to embrace assemblies for fear of being left behind economically by Scotland.
Citing the case of London, with an assembly and elected mayor, he will add: "It is quite possible to envisage a network of strong cities, or city regions, emerging to which powers could be devolved.
"We can then add into the mix historic counties with a strong local identity, such as Yorkshire or Cornwall."
He will say a US-style Senate, representing national and regional interests, would make the directly elected House of Commons work harder to agree and pass legislation. He will also say: "Federalism is very much an event, not a process. Once established, and codified in a written constitution, changing the ground rules in any direction would be extremely difficult, and therefore a more stable constitutional framework for the UK established."
The Liberal Democrats have long supported a federal constitution and, while not embracing the concept explicitly, a number of Labour figures have backed features of the system.
l SNP donor Sir Brian Souter's Stagecoach Group has warned investors about the potential "risks" of Scottish independence.
Changes to the regulatory environment or the availability of public funding as a result of the referendum, or from the subsequent UK General Election, "could affect the group's prospects", Stagecoach said in its preliminary results.