We present a procedure based on the combined use of analytical and numerical tools, useful for understanding the relative interplay between the various components of a free electron laser (FEL) self-amplified spontaneous emission (SASE) device. We take as reference case the Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC) experiment to analyze how electron beam transverse matching conditions affect the lasing conditions itself and discuss the possibility of implementing new configurations. In particular we show that the procedure can be extended to account for the effect of an on line inserted cavity, with the role of inducing a transverse longitudinal correlation allowing a transfer of the longitudinal and transverse emittance. We discuss the associated benefit on the FEL operation, with particular reference to the nonlinear harmonic generation. The possibility of completing the tool with regards to the beam degradation effects due to CSR is briefly accounted for.