After looking at the math, we should look at the politics. As you may have noticed, the Conservatives were over-represented. While the Tories do not win every rural riding, they do win a larger share of rural ridings than they do urban ridings. You may also notice the Greens were under-represented, this is a consequence of the small riding size (only 9 members) meaning that a party needs 11% to win a seat, and the Greens have yet to manage that over a large enough area. You'll also note my note about Simcoe County, which is that the math I've done shows results can be different. These three things are the key to allowing all 5 parties to back this. I will go one by one and examine why each party may, or may not, back this idea.
First, we need to be very clear what 'idea' we are talking about. The 'idea' I am proposing is based on something said by Jean-Pierre Kingsley, who pointed out that in the past, many provinces have had a form of PR. When I'd first heard of it, I dismissed it, and disagreed with it; but the more I thought about it, I've started to come around. It's far from my preferred idea, but it's something that I do not hate.
The idea itself is as follows
1 - "Urban" areas containing 3 or more ridings are combined into multi-member ridings.
2 - These "Urban" ridings should match municipal boundaries when plausible.
3 - These ridings should aim to contain 5 members each, but could have as many as 9 or few as 3.
4 - These urban ridings will use STV. Each voter has 1 ballot and ranks candidates preferentially.
5 - Rural ridings will continue to use FPTP.
As such, urban ridings will be similar to what exists in Ireland.
For the Liberal Party, this system allows them to achieve some of their goals. First off, the introduction of a preferential ballot in urban ridings will mean more Liberals elected. Even in my example, I did not do any STV calculations. As such, chances are we could see as many as 15 more Liberals win, and hence, possibly, retain their majority, though unlikely. This allows the Liberals to follow through on their promise to end FPTP, and due to the ranked ballot, likely improves the position of the party in all future elections compared to base PR. By adopting this, the party can claim a victory for Proportional Representation. It could also use this to justify making any further changes towards PR that would jeopardize the party's position. For a party that's yet to really take a stand for anything in particular on the electoral reform front, this allows the Liberals to sell this to caucus as well, telling the PR backers this is as good as it gets, and the FPTP backers that this is as little change as is possible.
For the Tories, a change from FPTP is risky. Keeping it in the rural areas of the country is an important selling point to them that will ensure they can back this. In fact, it is often the small c conservative party that walks away after an election with 0 seats in various large urban areas. This change means that will never happen again, as the Tories can be all but guaranteed MPs from large cities, only needing to win, for example, 20% of the vote to gain 1 MP in a 5 seat Riding. This can easily be sold as keeping bedrock blue ridings they way they are while allowing for the party to win previously unwinnable ridings. For the party, and their supporters, the fear of never having another Conservative majority again is what drives opposition to any change. By introducing a system that allows for a future Conservative majority, we can gain not just the party's members on the committee, and it's caucus in the house, but we can also gain the support of Conservative members and voters. This is crucial to winning any referendum on the issue.
For the NDP this might be the toughest sell. The party is strongly in favour of MMP-PR and will push for it whenever and wherever possible. For that reason, if the proposal I've outlined is moved forward, I strongly suspect the Liberals and Tories will use their combined majority on the committee to present the NDP with a difficult choice. They will make this proposal the only official proposal the committee is going to look at. In effect, they will tell the NDP to either back this proposal, or back nationwide FPTP. While the NDP will loudly complain, I suspect at the end of the day, they will comply, and back this proposal as well. As such, when this proposal leaves the committee, it will have the backing of all 3 of the national parties. I can also see the NDP backing this in a referendum, telling their supporters that some PR is better than no PR, and that the NDP will make MMP-PR a coalition issue after the first election using our new system (which will be more likely to produce minority governments).
For the Bloc, seen as an anti-PR party, there is an important gain to be made. The Bloc, for many years, won 50%+1 of all seats in Quebec. If you look from that perspective, it makes little sense to change. However, in the last two elections the Bloc has won 4, and 10 seats, less than 1/7th of the seats in the province. While this system will mean that we won't be seeing the Bloc sweeping the province, it also means that during the difficult times, the party has a base of support it can rely on. It is thus guaranteed to always have at least a few MPs in the commons so long as this system remains in place. Additionally, this system means it's possible for an anglophone Bloc member to be elected as an MP for anglophone Montreal. This is something the party would very much like to achieve. As such, I could see the Bloc back this, especially given their past historical successes in rural Quebec.
For the Greens, there seems to be no reason to back this on the surface, but that is when we get into something I've been eluding to for a while. My calculation is not a real election, it was a quick and dirty example. When New Zealand introduced Proportional Representation, voting patterns changed. We've also seen this in other areas that go from non-proportional to proportional systems. What that means, bluntly, is we could see the nationwide Green vote go from 5% to 10%. STV also means as candidates drop, the preference flows from other candidates can end up boosting someone to victory. With the Liberals and NDP being "parties of government" in many provinces, it's possible (likely in fact) that people may vote for a local Liberal/NDP MP they like #1, and preference a Green #2 because of perceptions of 'not caring' or outright corruption among the brass of their prefered party. The Greens, as such, would actually gain by a move to this new system, and would also be all but guaranteed a handful of MPs.
This is by no means a lock. It's quite possible no party will want to back this idea, especially if events back them into various corners. Nor is this the easiest path to a majority on the committee and in the commons. However; this is the most likely way to get all 5 parties on board, and to pass any referendum. Since it uses the existing map (simply 'clumping' existing ridings together) it is also something that can be done 'quickly' by the government, as oppose to having to take the time of redrawing the entire electoral map. When this has been used in the past in places like Manitoba and Alberta it has been abandoned after a few elections, but with more and more Canadians calling for PR, it's quite possible that when this system is replaced, it is replaced with another system that is far more proportional.