We study the spreading of cooperative infections in an empirical temporal network of
contacts between people, including health care workers and patients, in a hospital.
The system exhibits a phase transition leading to one or several endemic branches,
depending on the connectivity pattern and the temporal correlations. There are two
endemic branches in the original setting and the non-cooperative case. However, the
cooperative interaction between infections reinforces the upper branch, leading to a
smaller epidemic threshold and a higher probability for having a big outbreak. We show
the microscopic mechanisms leading to these differences, characterize three different
risks, and use the influenza features as an example for this dynamics.