In their search for different ways to create and capture value, INVs explore new value propositions; deploy value propositions in new segments, change the value chain, or experiment with alternative revenue models. In so doing, INVs exploration goes far beyond the existing business models. Their research results in the creation of new business models which are, to some level, contradictory to the existing models. The presence of multiple and contradictory business models within INVs pushes and pulls managers and organization actors in different directions as they are torn between these competing models. This paper aims at examining the multiple business model portfolio challenges for INVs beyond their early internationalization and how these challenges can be managed by utilizing a paradoxical framework. Based on a longitudinal qualitative study of three growing Swedish INVs—all of which have more than 80% of their turnover derived from sales outside of Sweden—the paper presents three paradoxes namely the innovation paradox, the focus paradox, and the boundary paradox that managers face as they explore new possibilities. The paper concludes that managers should develop a paradoxical mindset that [1] recognizes the contradictory business models, [2] embrace and accept tensions and contradictions instead of avoiding (or attempting to eliminate) them and [3] be comfortable enough that they use the tensions and contradictions as sources of energy for creativity creating and capturing more value to their firms. The paper further highlights that such paradoxical mindset is key to smoother business model exploration process and as such it contributes with new insight about growth and development of INVs over time.