The recently introduced TSCSTFCF start-up demonstration procedure is generalized to include multi-state tests (success, degradation, failure). The expected number of required tests and the probability of acceptance are evaluated. Comparisons to the previously known multi-state TSCS, CSTF and CSCF procedures, and to the binary TSCSTFCF procedure with i.i.d. tests are provided. A constrained optimization is presented for reducing the expected number of required tests subject to some constraints. Some reduction in the total number of tests is achieved for a correct choice of the relevant design parameters. Also, a procedure for estimating the possibly unknown probabilities of success, degradation and failure is presented using a maximum likelihood technique. Finally, it is pointed out how to extend the analysis for the case of nonidentical units.