This　work　extends　the　theory　of　backstepping　control　of　(m+n)　hyperbolic　PIDEs　and　m　ODEs　to　blocks　of　isotachic　states　(i.e.　where　some　states　have　the　same　transport　speed).　This　particular　yet　physical　and　interesting　case　has　not　received　much　attention　beyond　a　few　remarks　in　the　early　hyperbolic　design,　and　leads　to　a　block　backstepping　design.　Our　motivation　is　the　rapid　stabilization　of　N-layer　Timoshenko　composite　beams　with　anti-damping　and　anti-stiffness　at　the　uncontrolled　boundaries.　The　problem　of　stabilization　for　a　two-layer　composite　beam　has　been　previously　studied　by　transforming　the　model　into　a　1-D　hyperbolic　PIDE-ODE　form　and　then　applying　backstepping　to　this　new　system.　In　principle　this　approach　is　generalizable　to　any　number　of　layers.　However,　when　some　of　the　layers　have　the　same　physical　properties　(as　e.g.　in　lamination　of　repeated　layers),　the　approach　leads　to　isotachic　hyperbolic　PDEs.　We　use　a　Riemann　transformation　to　transform　the　states　of　N-layer　Timoshenko　beams　into　a　1-D　hyperbolic　PIDE-ODE　system.　The　block　backstepping　method　is　then　applied　to　this　model,　obtaining　closed-loop　stability　of　the　origin　in　the　L2　sense.　An　arbitrarily　rapid　convergence　rate　can　be　obtained　by　adjusting　control　parameters.　Finally,　numerical　simulations　are　presented　corroborating　the　theoretical　developments.　©　2024　EUCA.