I think you should make a distinction if the different behaviours comes from different circumstances or not.
If their environment is always the same, then I think the only to have what you ask is if the system has a hidden, very specific parameter, that says "when X and Y and Z happens, zig instead of zagging".
Otherwise, if the model is slightly chaotic, then an important alteration to the environment might provoke very different behaviour.

For the first type of agent, think of two Markov chains almost identical, only one has a very improbable arc to a stable subnet that doesn't exists in the other chain.
For the second type, think of two similar strange attractors, that have different behaviours away from the stable parameters. They will be approximately identical in the same zone and be very different away from that zone.