Highrises aren't necessary for density. Getting rid of parking and single-family homes is. Here's a look at a selection of European countries' most dense square kilometers.
https://www.theguardian.com/cities/g...-europe-mapped
For comparison, Winnipeg
might have a contiguous a square kilometer like these pictured with more than 10k people.
You won't see a lot of highrises in these satellite pictures. You also won't see parking lots or SFH zones. These cities are packing 20000-53000 people into one square kilometer, almost entirely in 3-8 floor buildings. And they do it over, and over, and over again. The key is to build midrises close together.
The area pictured that I'm most familiar with is part of Neukölln, in Berlin. On the ground, its built form is almost indistinguishable from any other industrial-era neighbourhood in Berlin--a solid streetwall of 6 story buildings. The density comes in behind the streetwall, where the hinterhofs (back yards or courtyards) are surrounded by more housing at the same scale. This gives the blocks their distinctive honeycomb appearance when seen from above.
While street level looks the same as many other areas, the experience is different. This is a very vibrant area, with bars, shops, and restaurants on every street. It doesn't need highrises.
Taking things back to Winnipeg, if you tipped over the Evergreen towers, they would fit on their massive parking lot as six story buildings with room to spare. They would house the same number of people. Their construction would have been cheaper. The urban environment would be better.
If you want more housing in OV, look at the Safeway parking lot, which could comfortably hold 600 units (as many as a sixty story tower) in six story buildings. Same with the parking lots along Gertrude. Same with the Dollarama parking lot at Confusion Corner.
Just by filling the neighbourhoods three biggest parking areas, we'd add housing for 5000 people. And it would be more affordable and make for a more vibrant neighbourhood than three sixty story towers (or six @ thirty, or nine @ twenty) ever would.
And that's without getting into all the wasted space along back lanes. Building a duplex in every alley parking lot would probably yield close to another 600 units.
If you want something to attack for holding the city back, go after parking minimums. Go after car culture, anti-urban setback rules, single-family zoning.