We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that n is not restricted to positive integers. For low activities of thevacancies, we observe critical points of the known universality class.At high activities the transition becomes first order. For n=0 themodel includes an exactly known theta point, used to describe a collapsingpolymer in two dimensions. When we vary n from 0 to 1, weobserve a tricritical point which interpolates between the universalityclasses of the theta point and the Ising tricritical point.