  Recently topological states of matter have witnessed a new physical
phenomenon where both edge modes and gapless bulk coexist at topological
quantum criticality. The presence and absence of edge modes on a critical line
can lead to an unusual class of topological phase transition between the
topological and non-topological critical phases. We explore the existence of
this new class of topological phase transitions in a generic model representing
the topological insulators and superconductors and we show that such transition
occurs at a multicritical point i.e. at the intersection of two critical lines.
To characterize these transitions we reconstruct the theoretical frameworks
which include bound state solution of the Dirac equation, winding number,
correlation factors and scaling theory of the curvature function to work for
the criticality. Critical exponents and scaling laws are discussed to
distinguish between the multicritical points which separate the critical
phases. Entanglement entropy and its scaling in the real-space provide further
insights into the unique transition at criticality revealing the interplay
between fixed point and critical point at the multicriticalities.
