My understanding is that the US has a two-party system because of single member districts and and winner takes all elections.Many Westminster descendants are not this way, and never have been. Canada has multiple parties, new ones crop up and old ones die.
The current conservative party is a 20ish year old party, and a merger/takeover of the Reform, then Alliance, the Conservatove party absorbing the tattered remnants of the old party.
We have political alliances, coalition governements where more than one party holds power, minority governments, and typically at least 3 main parties, with a smattering of others around.
We typically have 5 or 6 parties sitting at one time.
And yes, to the youngsters in the room, even our 3rd main party has held power from time to time.
But most importantly, party names and controllers change.
That's on the federal level. On the provincial level, new party spring with abandon, and form governments too.
What I would suggest, is not pushing for something incredibly insane sounding to most US ears, like changing the entire voting system, but instead just push for that third party, something that sounds more tenable.