LOL, I don't think Canada would allow you to have 2 passports valid at once.
You'd better arrange 2 days where you won't be travelling to renew it. The Government offers urgent pickup because people need their passports quickly, so if you are looking to skirt the fast processing fee by them just issuing you a new passport with regular processing time without you turning in your old one, it won't happen.
http://www.ppt.gc.ca/info/service.as...®ion=Canada
$110 extra for 24 hour processing. At least it'll be valid for 10 years.
And my advice is pay the extra for additional pages. I did on my recent renewal and it makes the passport a lot more durable as it resists bending.