Should I cook two pieces of Canadian Bacon twice as long as one in a microwave? It will probably depend on the size of the pieces... but at what point should I stop assuming a linear relationship?
I was prompted to ask in a previous question.
 A: My experimental evidence comes from baked potatoes.
1 potato takes 5 minutes to be at my liking
2 potatoes come out the same at 10 minutes
8 potatoes come out the same at about 35 minutes, i.e. less time per potato.If I let them go to 40 minutes (5x8) they become dry and wizened.
The total mass plays a role then.
A: To some approximation the whole cavity can be thought of as full of microwave radiation at some fixed power density. (Of course, we all know this approximation is weak 'cause some food has hot and cold spots, right?)
In that case, adding a second separate piece of food should have no effect, and you should use the same time for two pieces as for one. See the part of anna's answer about two potatoes.
However, this relies on the magnetron being able to keep the cavity flooded at a constant energy density even while the food is absorbing some of the power. It may be that the power will sag, in which case it will take a bit longer; that's the "many potatoes" part of anna's answer.
For a long time my rule of thumb was for $N$ pieces multiple the time by $1.5^{N-1}$, but I have begun to wonder if the base should be lower with my current machine.

Additional consideration: if your "extra" food is stacked or placed close together parts of it may shield other parts which almost certainly calls for more cooking time (perhaps at lower power).
A: Normally the heat losses increase with increase of the surface so you may have to cook even longer if the free surface is doubled. 8 potatoes put close to each other may have smaller free surface and get cooked faster than 5x8.
Ah, if you stuff your MW oven with too much of food that needs high temperature for cooking, then your temperature may become so low that cooking will take much more time.
A: Let's assume that heat losses are relatively insignificant comparing to heating power.
1:Microwave oven's power is likely to stay constant, but it's efficiency may increase with more bacon slices.
2:Roughly speaking, it will take time $t_1$ to heat up the food to 100 celsius , typically followed by time $t_2$ for the food to cook to whatever condition you find tasty (of course in practice it will also cook some during the heating up, and the $t_2$ may be zero). Doubling the power per bacon will only cut down the $t_1$ two times, but it won't cut down $t_2$ (and at the end of heating the bacon will be less cooked). 
Both of those things suggest that microwave oven will need less than twice the time for 2 bacons, even if heating time is twice as long.
However, if the bacon is considered cooked by the time it reaches 100 celsius in both cases the relationship will be closer to linear.
A: Bacon in the microwave oven is a real-world problem that does not reduce easily to a physical model. It is not clear what cooking bacon in the microwave actually means. Does it have to reach a certain internal temperature? Does it need be exposed to some above threshold temperature for a certain period of time to kill bacteria? Or maybe it needs to rapidly absorb a certain amount of energy per gram to break down the fibers and soften up? 
It would be easier if you asked about (and/or experimented with) boiling up water in the microwave. Water boils when it reaches 100 degrees Celsius, and that is very clear.  In this way, effects of cooling, feedback of load on efficiency, etc., can be isolated and investigated in detail. You can experiment with boiling up twice as much water in a glass vs boiling up two glasses of water (test the impact of cooling). You can try to boil up 1 cup vs 1 gallon (correct for the effect of cooling and learn if the extra load affects the power output). To avoid superheated water, you need to stop every minute and stir (see Superheated water on Mythbusters). And you must use fresh tap water every time so it contains the same amount of air.
