These are for Canada and the United States.
In the United States, separation of powers has caused the Presidency to absorb all of the attention during election time. This is the key aspect that needs fixing. As a result, the simple proposal I have is to replace the Electoral College with Congress.
This means the total number of Senators and House Representatives each party gets will determine which party's candidate wins the Presidency.
It will force the parties to have a consistent policy and to pick someone they can work with.
In Canada, we sort of need the opposite. So much attention is paid to the Prime Minister, we should be electing them directly. Therefore, added to a proportionally elected house, would be a "slate" of candidates.
Each slate would be lead by a candidate for Prime Minister. Each slate would have 34 other members in it, chosen by the party.
All 45 of these candidates would also be running in individual ridings. Like the Montreal system, each of these people would have a "co-candidate" or "running mate" who will take the seat should the person be elected to the Slate and not the Riding.
Canadians would vote not only for MP, but also for which slate they feel should win. The slate elections would be preferential, and whichever slate (and Prime Minister candidate) wins 50%+1 of the vote, gets elected to Parliament in addition to all the MPs.
As a quick and dirty example, lets presume the last election, proportionally, elected 147 Liberals, 118 Tories, and 73 New Democrats. Now lets presume Trudeau's slate wins.
This produces 192 Liberals, 118 Tories, and 73 New Democrats, a very narrow majority.
In effect, if the Prime Minister is able to get 40% of the country to vote for him, he can get a majority in the house. Canadians main concerns about PR is that it would mean endless minority governments; this helps fix that.