This paper develops a novel formal semantics of ideophones that can account for their meaning and compositional properties. The proposal extends recent work on iconicity in sign languages in Davidson (2015), whose demonstration- based framework provides a formal foundation for the semantics of ideophones that captures the difference between descriptive meaning and depictive meaning, the kind of meaning ideophones traffic in. After providing a demonstration-based account of the basic ideophone construction in the Mayan language Tseltal, the paper then shows how the demonstration-based account can be used to analyze pluractionality in the ideophone domain. In particular, through case studies on Tseltal and Upper Necaxa Totonanc (Totonacan), I show that there are two previously unrecognized types of ideophonic pluractionality, and that their properties support the demonstration-based account.