  This paper introduces a novel approach for the construction of bulk--surface
splitting schemes for semi-linear parabolic partial differential equations with
dynamic boundary conditions. The proposed construction is based on a
reformulation of the system as a partial differential--algebraic equation and
the inclusion of certain delay terms for the decoupling. To obtain a fully
discrete scheme, the splitting approach is combined with finite elements in
space and a BDF discretization in time. Within this paper, we focus on the
second-order case, resulting in a $3$-step scheme. We prove second-order
convergence under the assumption of a weak CFL-type condition and confirm the
theoretical findings by numerical experiments. Moreover, we illustrate the
potential for higher-order splitting schemes numerically.
