Can I run migration assistant multiple times for multiple computers?
Without the source or the full functionnal specification from Apple it is impossible to give you an answer with no risk.

To clarify your question let's say your 3 Macs are named A, B and C.
A being the oldest one, then B, and C the younger one.

Your question is "can I run Migration Assistant this way":

A → C
and then
B → C


I am convinced that Apple didn't take into consideration such a scheme of migration which might lead to data loss or corruption.

On the other hand, if you want to run Migration Assistant this way:

A → B
and then
B → C


I am convinced that the integration process will work correctly on B and then on C.
In this case, make a full backup of B before starting.