In　this　paper,　we　investigate　the　rapid　stabilization　of　two-layer　Timoshenko　composite　beams　with　anti-damping　and　anti-stiffness　at　the　uncontrolled　boundaries.　This　work　extends　our　previous　result　on　single-layer　Timoshenko　beams.　While　the　problem　of　stabilization　for　two-layer　composite　beams　has　been　previously　studied,　the　obtention　of　an　arbitrarily　fast　decay　rate　is　a　novel　result,　as　well　as　considering　anti-damping　and　anti-stiffness　in　the　boundaries　(which　can　possibly　lead　to　rapid　divergence).　Our　approach　is　based　on　the　introduction　of　a　Riemann　transformation　of　the　states　of　two-layer　Timoshenko　beams　into　a　1-D　hyperbolic　PIDE　(partial　integro-differential　equations)-ODE　system.　Then,　PDE　backstepping　is　used　to　design　a　control　law　resulting　in　closed-loop　stability　of　the　origin　in　the　L2　sense.　An　arbitrarily　rapid　convergence　rate　can　be　obtained　by　adjusting　control　parameters.　Copyright　(c)　2023　The　Authors.