From the Bose-Einstein distribution it follows that a non-interacting Bose gas condenses into the Bose-Einstein condensate below a certain critical temperature. What happens when interactions are introduced in a Bose gas is not dealt with in introductory Statistical mechanics courses. Hence my questions are pretty naive and basic.
How is(are) the interaction(s) quantitatively modelled in a Bose gas and how does it change the behaviour (compared to the noninteracting Bose gas) when the temperature is lowered? Is there a way to physical understand the change in the behaviour, if any?
As a minor comment, I have been informed that in case of Fermi gases, the role of interactions shifts the effective mass from $m\to m^*$ and the energy levels (effectively mapping the interacting system to a system of quasiparticles that still obey FD statistics). Does the similar thing happen here too?