In the US, universities use the term "Institute" mostly as marketing. They can take existing related units and organizations within the uni and package them under the term Institute for the purposes of creating a single cohesive brand for said discrete parts. The point of this is to be able to more easily solicit funding now that you have a more cohesive description of these areas under one identifier. It sounds strange, but after seeing it work first hand I get it now, it can also help fund areas that may be underfunded.

So, taking that knowledge, you can potentially collaborate with other existing organizations to help build your institute "brand" which can help further your mission. You might consider a discrete research lab as a separate entity under your broader institute brand. Collaborating with other existing groups is a powerful way to amplify your impact as well as easy publicity for your larger mission.

Just some food for thought.