Yes. The choice of tailoring variable (i.e., what gets monitored during the next stage of intervention) can, itself, be part of a decision rule in an adaptive intervention.

In the hypothetical adaptive intervention below, the first-stage decision rule recommends (i) different first-stage treatment options (namely–low-dose medication for high severity children vs behavioral intervention for lower severity children), as well as (ii) different approaches to monitoring during the first-stage of intervention (namely–symptom reduction for children offered medication vs improvements in target behaviors for children offered behavioral intervention).