Summary: ``This paper deals with the existence of multiple positive solutions for the quasilinear second-order differential equation $$ (\phi_p(u'(t)))'+a(t)f(t,u(t))=0,\quad t\in(0,1), $$ subject to one of the following boundary conditions: $$ \phi_p(u'(0))=\sum^{m-2}_{i=1}a_i\phi_p(u'(\xi_i)),\quad u(1)=\sum^{m-2}_{i=1}b_iu(\xi_i), $$ or $$ u(0)=\sum^{m-2}_{i=1}a_iu(\xi_i),\quad \phi_p(u'(1))=\sum^{m-2}_{i=1}b_i\phi_p(u'(\xi_i)), $$ where $\phi_p(s)=|s|^{p-2}s$, $p>1$, $0<\xi_1<\xi_2<\dots<\xi_{m-2}<1$, and the nonnegative constants $a_i,b_i$ ($i=1,2,\dots,m-2$) satisfy $$ 0<\sum^{m-2}_{i=1}a_i<1\quad \text{and}\quad 0<\sum^{m-2}_{i=1}b_i<1.$$ Using a five-functionals fixed point theorem, we provide sufficient conditions for the existence of multiple (at least three) positive solutions for the above boundary value problems.''