There are plans on the net but I don't have any saved. Even if you can't find them a reptile cage is typically a simple box so not a lot is needed in the way of plans.
One design feature I would recommend is to make the inside length a bit over 48". This will allow you to easily install 48" light fixtures which are brighter and have more bulb options for diurnal lizards. Even if you plan to use something other than fluorescents I would leave the space for 48" bulbs as you never know when some of the smaller bulb options we have today will not be availble to the average consumer.
Given that most sheet goods come in 48x96 sizes this is not always easy without a lot of waste. Melamine and MDF both come in 1" oversized sheets -- 49" x 97"" -- so they work well. They are inexpensive but also very heavy.
You can still use lighter plywood but may have more waste. Or you can build them in a way that allows a 48" light fixture to be installed on a diagonal. If I remember correctly, this means a cage deeper front-to-back than 24".
Another option is to simply notch out one side so the light fixture can protrude through the cage slightly. Something will need to be done to keep insect prey items from escaping.
When I think of a bearded dragon cage I assume substantial substrate depth which means a lot of weight. As such most plastics are not sufficent, IMO, for a stackable cage as you mentioned.
There are extruded hollow core PVC products that are available and I suspect they would allow for a stackabe cage with a deep substrate. I would assume these will be just under $4 per square foot once you factor in shipping.
Melamine would probably be just a bit over $1 per square foot picked up locally.
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Currently keeping:
6.10 Gonyosoma oxycephalum (Javan, mixed colors)
1.1 Philodryas baroni
1.1 Lampropeltis triangulum multistriata
1.0 Rhodesian Ridgeback