Yes!! You can conduct project in team, with people within or outside your university.
Sometimes also, it happens that massive workshop/ seminars are organised in some university, gathering for a few weeks or months all the people in some research area in order to solve a big problem in the area and conduct an important project.
Yes, researchers often team together to work on big projects. A good example is CERN, which is an institute using a particle accelerators to understand what the universe is made of.
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