Your plate isn't microwave safe

If you have a poor quality, low density (often mass produced), ceramic plate, there are tiny air bubbles inside it. These vibrate when the microwave runs, heating the plate faster/more than the food. This is the same reason why some mug handles get hot enough for 2nd or 3rd degree burns in the microwave while others never get the "microwave handle of death". Better made ceramics will have far fewer (or none) of these bubbles. This is why usually hand made pottery will not heat up like this, while factory stuff that was quickly poured into molds often will.

Food is full of water and takes a lot of energy to heat up. The plate is thin and made of easily heated material like ceramic or glass.

Your plate isn't microwave safe and is absorbing the energy.

Every microwave has a specific 3d radiation wave harmonic pattern which determines the power distribution within the volume of your microwave enclosure. Most microwaves are strongest slightly to the left of center.

If you want to test, put a full plate of mashed potatoes or something in your microwave, without the turntable. After a couple mins take some temp readings at spots on the plate.

That would imply that there is moisture inside the plate ceramic.

[Edit: I went and read a scientific article about this and actually a lot I wrote here is wrong. Basically microwaves work by heating the water in the food by making the water molecules oscillate with the waves. (Ref: http://www.sfu.ca/phys/346/121/resources/physics_of_microwave_ovens.pdf skip the part about how a magnetron generates microwaves and how frequencies are limited by the dimensions of the waveguide if all you care about is how the heating works). It's not at all the mechanism I thought and my conclusions are all off. This would mean that as somebody pointed out it's the humidity in the plate causing it to heat, which woukd explain why it happens with earthware.

The bit about which plates work best or not for me is correct as it's experimental, as is the thermal conduction stuff because I actually learned that at Uni rather than presumed from what I knew (a totally different mechanism were photons are actually absorbed, which is not at all how microwaves heat food)]

~~It's to with the relative ability of materials inside that microwave to absorb that frequency of microwaves: the microwaves just bounce around in that compartment until they get absorbed, and those materials with a higher absorption ability for microwaves at the frequency used in microwave ovens ("microwave" is a whole range of frequencies and those ovens are tuned to emitting just a specific frequency) will end up "taking" a higher proportion of them (and hence of energy) than the other materials and thus heat up more.~~

~~If the difference in absorption rates is big enough you end up with a situation where one things is absorbing 90% (or a similarly large fraction) of the energy bouncing around as microwaves in that oven and leaving only a smaller fraction for the rest, and hence heating up a lot more.~~

~~You get a similar thing if you put, say, cheese on toast next to a glass of water in your microwave oven: that cheese, which is mainly fat, will melt like crazy and the water will barelly have heated up, because water is nowhere as good as fat in heating up (I believe, but am not sure, that the actual frequency chosen in the microwave spectrum for use in microwave ovens was the one that fat best absorbs)~~

~~That plate of yours probably is some kind of ceramic material with metal particles in it, so it's better at absorbing the microwaves than the food, hence the plate captures most of the microwaves (so, most of the energy pumped into that chamber), hence heats up much more than the rest.~~

The termal conduction between the materials with different microwave absorpion rates that heat differently in that microwave will tend to equalize the temperature over time, but unlike with the fat which is part of the food itself and thus will quickly equalize temperature with all the other stuff around it (such as with the water in the food but not, as in my example above, water in a glass which is separated from it), the food and the plate are only in contact is a very limited area (were the food touches the place) so the temperature equalizes much slower between both.

Try a different kind of ceramic (in my experience that problem happens mostly with earthware, so try finer ceramic materials) or glass plates.

In the meanwhile if using the current plates, you can just use a lower power setting in that microwave oven to give more time for the above mentioned process of the temperature equalizing by conduction to move the heat from the plate to the food, spread the food better on the plate to have a higher the area of contact and thus more the thermal conduction for heat transfer between plate and food, or just leave the plate there with the food for a little while after the heating cycle is over so that more of the heat is conducted from the plate to the food before you take it out.

If the glaze on a ceramic plate has micro cracks on it, it can cause water to get inside the plate, which then gets hot in the microwave. Throw it away, it can grow bacteria.

Twice the time at half the power solves most microwave heating issues.

I almost always find the solution to microwave reheating issues is to add water before reheating because that's primarily what the microwave is heating up.

Improperly aligned waveguide.

Your plate has lead in it. Get new plates.

I've never had this issue

How does that even happen? I thought only strongly polar molecules interact with microwaves. What exactly in the plate is polar?

The plate is a black hole and the food is a white hole. Thanks for joining my TED talk.

Personally I've found it's quite dependent on the plate color it's actually the reason why all my mugs are black. Red and white really like to exsorbe the microwaves

Don't use metal-coated plates