From an immigration and customs point of view, this is perfectly possible. Assuming any connection of the type <Not Canada>–YVR–YYZ, you would face entry immigration at YVR and then, according to Canadian law, pick up your bags, pass through customs and recheck them onto the flight to YYZ (Toronto). Once you have performed these first two steps you are in Canada and nothing is stopping you from going out of the airport, meeting your friends, hitch-hiking to the Yukon or whichever other you ideas you come up with instead of taking the immediate flight to Toronto.
Furthermore, when you return to the airport for the next day flight YVR–YYZ, it’s all within Canada so it’s simply drop off bags at check in, go through security, proceed to gate, fly and get out; no need for any passport unless if you use it as an identity document at check in.
The main ‘issue’ you will face will be booking the flight(s), especially if you have some sort of grant or stipend that will pay for or towards your travel cost. If there is any requirement for the flight from Bangladesh to Toronto to be on a single ticket for these grants to be applicable you will have to book them on a single ticket. It’s not impossible to get long layovers of e.g. 24 hours with onward tickets (I personally have enjoyed FRA–YYZ–YVR (overnight)–SYD and return as well as MUC–HEL (overnight)–KIX) but sometimes the online booking system may hiccough and you may need to talk to an agent on the phone or in person.
If you do have a through ticket with a long layover, you will have to ask the check-in staff to short check your bags to Vancouver rather than all the way to Toronto. Since you have an overnight layover, this should not be an issue (it can be for shorter, non-overnight layovers as the airline staff may suspect hidden city ticketing).
For this scheme to work on a single ticket, however, you need to make sure that your flight will actually pass through Vancouver on the way to Toronto. Plugging random dates into Google Flight, there seems to be no big difference between going westwards (e.g. Emirates or Turkish) and eastwards (e.g. China Southern, Cathay Pacific). If you go westwards, you will hit Toronto before you hit Vancouver so I will imagine it to be a pain in the backside to get a flight via Vancouver. If you go eastwards, you need to make sure that there is actually a layover in Vancouver, as e.g. China Southern and Cathay Pacafic also have direct flights to Toronto from Asia and at least one connection uses Tokyo–Toronto which will also be of no use to you. Thus: make sure before choosing an airline (combination) that it will actually go your way and all is feasible on a single ticket.
Finally, there is the option of getting two tickets. This may be easier to book especially if you don’t have any requirement to have the entire Bangladesh–Toronto route on a single ticket as you can choose the layover in Vancouver according to your requirements. Note that it may be more expensive than a single itinerary on a single ticket! If you do have two tickets, you can go westwards or eastwards as your first ticket will bring you to Vancouver either way but it is probably more convenient to still take the eastwards route as then likely your first Canadian port of entry will be Vancouver.
You should be aware about immigration when choosing this route, though. They will likely expect you to have a ticket all the way to Toronto if you first enter Canada in Vancouver and they will, obviously, question you to see if your answers match up with the presumed intent according to your visa. Now your visa will say student and you will obviously have the papers or other proof of the college in Toronto so they will likely ask you whether you will be taking the next flight to Toronto. Obviously you will say no (Please do not ever, ever, ever lie to immigration or customs!) which will immediately cause a raised eyebrow and you will need to explain your situation (you are visiting friends, seeing the city, etc). I strongly recommend you to have proof of your ticket Vancouver–Toronto ready to present to the immigration officer to prove your story of being a real student on their way to their proper place of study getting ready for their semester. Thankfully, as you have already been granted a mid-term visa you really only need to convince the guy that you do intend to move on to Toronto soon and not go underground in Vancouver.
Tl;dr: Yes, what you plan is possible but you will need to plan it properly and potentially argue accordingly at immigration.