Interval Markov Chains (IMCs) are the base of a classic prob-abilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters. In particular, we propose constructions for the synthesis of all parameter values ensuring several properties such as consistency and consistent reachability in both the existential and universal settings with respect to implementations. We also discuss how our constructions can be modified in order to synthesise all parameter values ensuring other typical properties.