Tactical voting to beat the Tories: does the maths equal a coalition?

Every few years, someone suggests forming a progressive coalition to beat the Conservatives. Could a Lib/Lab/Green alliance really beat Theresa May?

Every time there's an election, which is often, some bright spark on the left comes up with an amazing idea. "There are the Tories, right, and Labour, who are trying to stop them, and then there are all these other parties like the SNP and the Lib Dems and Caroline Lucas and the Welsh one. So here's a thought: what if they all clubbed together and just decided to beat the Tories?"

It's a compelling thought, if you ignore political reality and you can genuinely imagine Nicola Sturgeon playing Nick Clegg to a Prime Minister Corbyn. If you could get the so-called 'progressive coalition' of Labour, the Lib Dems, the SNP and the Greens to vote in perfect harmony, with all their existing supporters voting tactically in perfect harmony to keep the Tories out in each seat, what would actually happen?