In randomized controlled trials, the complier average causal effect (CACE) parameter is often of policy interest because it pertains to intervention effects for study units that comply with their research assignments and receive a meaningful dose of treatment services. Causal inference methods for identifying and estimating the CACE parameter using an instrumental variables (IV) framework are well established for designs with a single treatment and control group. This article uses a parallel IV framework to discuss and build on the much smaller literature on estimation of CACE parameters for designs with multiple treatment groups. The key finding is that the conditions to identify and estimate CACE parameters are much more complex for multiarmed designs and may not be tractable in some cases. Practical steps are provided on how to proceed, and a case study demonstrates key issues. The results suggest that ensuring compliance is particularly important in multiarmed trials so that intention-to-treat estimates on the offer of intervention services (which can be identified) can provide meaningful information on the CACE parameters.