It was recently found that, going beyond the tenfold Altland-Zirnbauer symmetry classes and violating the bulk-boundary correspondence of the usual topological phases, $\mathcal{P}\mathcal{T}$-invariant systems support a real Chern insulator with the so-called boundary criticality, which forbids the transition between different orders of topological phases accompanied by the touching of bulk bands. Here, we find that periodic driving can break the boundary criticality of a $\mathcal{PT}$-invariant system. Upon setting the system free from the boundary criticality, diverse first- and second-order topological phases absent in the static case are found in both the zero and $\pi /T$ modes. In contrast to the usual Floquet ones defined on stroboscopic dynamics, our topological phases can only be characterized by the dynamical process of a whole driving period. The application of our result in a three-dimensional $\mathcal{PT}$-invariant system permits us to discover exotic second-order Dirac and nodal-line semimetals with coexisting surface and hinge Fermi arcs. Enriching the family of topological phases in $\mathcal{PT}$-invariant systems, our result provides a useful way to explore novel topological phases.

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• Symmetry protected topological states
• Topological phase transition
• Floquet systems
• Nodal-line semimetals
• Topological insulators