Multistep DBT and regular rational extensions of the isotonic oscillator

► Hamiltonian hierarchies via SUSY quantum partnership generalized to excited states. ► Goes beyond the scope of the Crum and Krein-Adler theorems. ► Complete proofs based on deconjugacy theorems and recurrency scheme. ► Determinantal expressions for new exceptional Laguerre polynomials. ► Proof of the hereditary character of the shape invariance.