  We consider the problem of constructing multiple conditional randomization
tests. They may test different causal hypotheses but always aim to be nearly
independent, allowing the randomization p-values to be interpreted individually
and combined using standard methods. We start with a simple, sequential
construction of such tests, and then discuss its application to three problems:
evidence factors for observational studies, lagged treatment effect in
stepped-wedge trials, and spillover effect in randomized trials with
interference. We compare the proposed approach with some existing methods using
simulated and real datasets. Finally, we establish a general sufficient
condition for constructing multiple nearly independent conditional
randomization tests.
