Can I case different strains in the same casing container?

Yes, you can in theory.
If you do it, place each strain in it´s own sector of the container, don´t mix the substrates together. If you do it nevertheless, you will get many, many small mushrooms of each strain scatered throughoput the casing, since the substrate won´t grow to a block and thus won´t be able to produce big fruits, but only small ones from the local accumulations of the different strain´s mycelia.

BUT: Different strains have different speeds of growth and thus you will have difficulties adjusting the required temperature and humidity requirements, since the cycles of both strains will be different.
Another thing that speaks aginst it is that you can easily confuse the strains this way, something that shouldn´t happen if you attend to take prints and possibly share or trade those prints among your fellow growers.

All in all: don´t do it, better place each strain in its own container.

P.S.:
Sometimes you might hear people saying something along the lines of "don´t mix 2 strains in a casing, they will compete for nutrients...".
That´s nonsense.

Once you are at the stage of casing a substrate, the substrate is already colonized(not completely digested of course, but at least the outside of the substrate kernels is encompassed) by either the one or the other strain. So they won´t compete for any nutrients, the nutrients are already allocated. woot