  We address the possibility of realizing Bose-Einstein condensation as a
first-order phase transition by admixture of particles of different species. To
this aim we perform a comprehensive analysis of phase diagrams of two-component
mixtures of bosons at finite temperatures. As a prototype model, we analyze a
binary mixture of Bose particles interacting via an infinite-range (Kac-scaled)
two-body potential. We obtain a rich phase diagram, where the transition
between the normal and Bose-Einstein condensed phases may be either continuous
or first-order. The phase diagram hosts lines of triple points, tricritical
points, as well as quadruple points. We address the structure of the phase
diagram depending on the relative magnitudes of the inter- and intra-species
interaction couplings. In addition, even for purely repulsive interactions, we
identify a first-order liquid-gas type transition between non-condensed phases
characterized by different particle concentrations. In the obtained phase
diagram, a surface of such first-order transitions terminates with a line of
critical points.
