Excitation energies of the ns, np, nd, and nf (n <= 9) states in Li-like Be+ are evaluated within the framework of relativistic many-body theory. First-, second-, third-, and all-order Coulomb energies and first-and second- order Breit corrections to the energies are calculated. Two alternative treatments of the Breit interaction are investigated. In the first approach, we omit Breit contributions to the Dirac-Fock potential and evaluate Coulomb and Breit-Coulomb corrections through second order perturbatively. In the second approach, we include both Coulomb and Breit contributions on the same footing via the Breit-Dirac-Fock potential and then treat the residual Breit and Coulomb interactions perturbatively. The results obtained from the two approaches are compared and discussed. All-order calculations of reduced matrix elements, oscillator strengths, transition rates, and lifetimes are given for levels up to n = 9. Electric-dipole (2s-np), electric-quadrupole (2s-nd), and electric-octupole (2s-nf) matrix elements are evaluated in order to obtain the corresponding ground-state multipole polarizabilities using the sum-over-states approach. Recommended values are provided for a large number of electric-dipole matrix elements. Scalar and tensor polarizabilities for the ns, np(1/2), np(3/2), nd(3/2), and nd(5/2) states with n <= 9 are also calculated. The scalar hyperpolarizability for the ground 2s state is evaluated and compared with the result of a nonrelativistic calculation. DOI: 10.1103/PhysRevA.87.032502