In an ecological system, pathogens often need to share their host with other pathogens, and therefore compete for the resources with different spreading strategies. Both cooperative and competitive interactions in bacterial infections have been observed. Here we first review recent theoretical studies addressed these two mechanisms separately and then study their combination and discuss about non-trivial dynamical effects can be expected to arise. Thus we study two strains competing with each other for host resources in the presence of a third pathogen cooperating with both of them. We first treat dynamics in a homogeneously mixed population by means of mean-field theory and stability analysis. We study the impact of cooperation on the outcome of the two-pathogen competition, which can be quantified in terms of dominance of one competing pathogen or the co-circulation of both of them. We show that the presence of a third cooperating pathogen can alter the outcome of competition as it may favor the more cooperative pathogen over the more infectious one. We then consider more complex contact structures among hosts and perform computer simulations to study the evolution of the diseases.