  This paper investigates the observational capabilities of monitors that can
observe a system over multiple runs. We study how the augmented monitoring
setup affect the class of properties that can be verified at runtime, focussing
on branching-time properties expressed in the modal mu-calculus. Our results
show that the setup can be used to systematically extend previously established
monitorability limits. We also prove bounds that capture the correspondence
between the syntactic structure of a branching-time property and the number of
system runs required to conduct the verification.
