Hackers Help: Bunk bed using 4×4 Kallax?

Has anyone ever tried creating a “bunk bed” using two 4×4 Kallax shelves? Do you think that two units, one at the head of the bed and one at the foot of the bed, with an Ikea Fjellse single bed frame on top would work? Of course, the Kallax shelves would need to be diagonally braced with  Observator cross-braces, and all three units connected together with brackets or something. With this setup, you would almost have a mini-room underneath the bed, which could be used as a study space with the addition of a desk.

I’ve seen photos of people making storage beds with 2×4 Kallax shelves laid horizontally underneath the bed, but never anything made with 4×4 shelves. Too unstable maybe?

Any feedback would be appreciated.

Heath