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A method to construct multi-indexed exceptional Laguerre polynomials usingisospectral deformation technique and quantum Hamilton-Jacobi (QHJ) formalismis presented. We construct generalized superpotentials using singularitystructure analysis, which lead to rational potentials with multi-indexedpolynomials as solutions. We explicitly construct such rational extensions ofthe radial oscillator and their solutions, which involve exceptional Laguerreorthogonal polynomials having two indices. The exact expressions for the $L1$,$L2$ and $L3$ type polynomials, along with their weight functions arepresented. We also discuss the possibility of constructing more rationalpotentials with interesting solutions.

QHJ route to multi-indexed exceptional Laguerre polynomials and corresponding rational potentials