Can't comment yet, so here's my first ever answer!
My old, really old, Pixma used to have a colour calibration feature where it'll print off a test page with tables of hundreds of coloured squares that could then be put into the scanner and it would calibrate the printer; if that still exists in Canon Pixma printers?
If the monitor has been calibrated, and your prints still aren't right, you could just adjust the values in the "printer driver utility"/"custom ICC profile"/"operating system colour manager" options instead, using a test sheet as a reference (or Pantone/other colour swatches, I've heard people using Dulux swatches on a budget/free), both physical and from their website if you don't have a hardware calibration tool).
- Match the physical swatch/colour card to the monitor/digital version.
- Match a new, stable, print of those same swatches to the monitor.
- Adjust the "driver utility"/"ICC profile"/"operating system settings" accordingly until it matches as close as possible.
I've noticed that the types of papers you print on can make a difference too, I used to have separately calibrated, regularly updated profiles for different mediums. I've not made print for a while, but I recall the glossy paper that I used made my pictures have a mild yellow/green cast and one type of matte paper always left things slightly blue for example. Each change needed a profile that wanted updating often.
It's also worth noting the importance of ambient light. Again about stressing calibration; I have a 5500 kelvin 125w bulb as an ambient working light, this is amazing to work with. However, I also have a 6700 kelvin 125w bulb which vastly changes everything. I have over 10 calibrations for my monitor alone covering daylight, different bulbs, web images, product images, and whether it's day or night. I just rotate and keep them updated every 2-4 weeks, and each photoshoot starts with a colour chart calibration photo to dial in the lighting/colour for that shoot. Proofing can be hard work!
All that aside, I have never had more issues than I did with inks, before the final straw I just bought larger quantities and topped them up by making a small hole in the cartridge and using a large hypodermic needle. Although even this became tedious after so long with cartridges being chipped to say empty and stop the printer working even though they were full (not sure whether this applies to other printers or just the one I had). Of course this was 5-7 years ago too, things may be different now.
In the end I cheated and now get everything printed somewhere else :P
I'm sure there's tonnes more I've missed or not explained correctly, but sleep awaits!