We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns.