Organizations often launch exploration projects (EP) aiming at developing innovative products (or services) by the exploration of new technologies, users, ecosystems or business models. Because a fundamental purpose of any project is to create value, the approach of value management (or value engineering) has been largely adopted in the organizations to manage the projects. However, the fact to move beyond the existing markets and the established technologies imply great difficulties and uncertainties for managing creative projects. Indeed, because exploration projects precisely aim to invent products (or services) that do not exist before, the value to create is unknown at the start of such project. So, what does value management precisely mean in situation of exploration project? This research aims to clarify the nature, the beneficiaries, and the ways to manage the value in such situations. After reviewing the historical development of the two traditional approaches of value management in project management literature, we then show we show their inadequacies for managing exploratory situations. This article is based on a longitudinal of two case-studies into a collaborative management research conducted with a major French car manufacturer. The two case-studies are an inter-firm EP corresponding to the joint exploration of an innovative multimodal urban platform by the automotive firm and two other industrial partners and an intra-firm EP aiming at generating innovative projects for the development of the electric vehicles. We propose an expansive value management model (EVM) towards three main propositions: 1) evaluating and stimulating the creation of value with a constant comparison with the dominant designs - (2) sustaining the exploration by tuning the degree of undecidability - (3) stimulating the emergence of new ecosystems by the creation of new platforms projects. Finally, this research proposes key managerial principles for EP management and a set of indicators to monitor the exploration process (i.e. identifying design rules to break, managing two kind of design paths...) and the collective dimension (i.e. the beneficiaries...) of EP.