This comes up from the desire to operate a plane (registered as an amateur built) as an ultralight on wheels and as a traditional amateur built when on floats.
How it works is that when you get the special C of A, you apply for the maximum weight you will want to operate from in that configuration, and do the climb test at that weight. Then when you add (or remove) the floats, you do all the major mod paperwork, apply for a flight permit to do the climb test in the new configuration at the new weight, and then after submitting the results of the climb test and all the major mod paperwork TC will send you a new C of A with the highest of the two weights. Then it's up to you to figure out a way to stay safe and legal when changing configurations in the future.
As for changing the registration of the aircraft, I don't know what the rules are for registering an ultralight so I can't comment. After you register the aircraft as an ultralight, I think you would have a very tough time getting it registered again as an amateur built aircraft. You would need a new C of A after another inspection, and how could you prove that the airplane meets all the requirements for amateur built if it's been flying around as an ultralight? Even if you found an MD-RA that would sign off on the aircraft, TC would issue you with a C of A with restrictions for the first 25 hours. It's just not a practicable idea.
In terms of flying as an ultralight, my understanding is that any aeroplane - regardless of the category it is registered under - that meets the definition of an ultralight airplane (ie 1232lbs gross, 45mph stall...) can be flown by an ultralight pilot. But that same plane, in theory, could be flown IFR, at night, for flight training etc... by someone who processes an RPL PPL CPL and is qualified to do so.
However, it seems that if that more qualified pilot wanted to fly it heavier than a 1232lb (on floats for eg.) they would need to register the plane having a higher gross weight and then the plane would no longer be able to be piloted by an ultralight pilot.
Every time you swap between wheels and floats, you could re register the gross weight between 1232lb and 1500lbs, but I guess this would entail a fair bit of paperwork each time.
That would surprise me but I can't think of which CAR you would be breaking so I suppose it's possible.
If you leave it registered as an amateur built aircraft it would only be a major mod once. After Transport Canada has accepted the two different gross weights, it's a single line tech / journey log entry. There is no need to change the registration.