We study boson star configurations with generic, but not nontopological, self-interaction terms. When compared with the usual λ|ψ|⁴ potential, similar results for masses and number of particles appear. However, changes are noticed in the order of a few percent of the star mass. We explore, using catastrophe theory, the stability properties of the configurations and look for possible observational outputs that may differentiate one model from the other: gravitational redshifts, rotation curves of accreted particles, and lensing phenomena are computed for our new cases.