  Multitime Landau-Zener (MTLZ) model is a class of exactly solvable quantum
many-body models which is multitstate and multitime generalization of the
two-state Landau-Zener model. Currently discovered MTLZ models include the
"hypercubes", the "fans" and their direct product models. In this work, we
prove two no-go rules, named the "no $K_{3,3}$" rule and the "no $1221$" rule,
which forbid the existence of exact solutions for models with certain
structures of interactions. We further apply these rules to show that for
models with no more than $9$ states, besides the models mentioned above there
are no other MTLZ models. We also propose a scheme to systematically classify
cases that could possibly host MTLZ models. Our work could serve as a guideline
to search for new exactly solvable models within the MTLZ class.
