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We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t)+h(t)f(t,u(t))=0, cr u(a)=alpha u(b)+delta u^Delta(a),quad eta u(c)+gamma u^Delta(c)=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0<alpha<frac{c-a}{c-b}$ and $bin(a,c)subsetmathbb{T}$.