  The logarithmic correction for the order of the maximum of a two-type
reducible branching Brownian motion on the real line exhibits a double jump
when the parameters (the ratio of the diffusion coefficients of the two types
of particles, and the ratio of the branching rates the two types of particles)
cross the boundary of the anomalous spreading region identified by Biggins.
  In this paper, we further examine this double jump phenomenon by studying a
two-type reducible branching Brownian motion on the real line with its
parameters depend on the time horizon t. We show that when the parameters
approach the boundaries of the anomalous spreading region in an appropriate
way, the order of the maximum can interpolate smoothly between different
surrounding regimes. We also determine the asymptotic law of the maximum and
characterize the extremal process.
