Fast Iterative Pixel Purity Index (FIPPI) was previously developed to address two major issues arising in PPI which are the use of skewers whose number must be determined by a priori and inconsistent final results which cannot be reproduced. Recently, a new concept has been developed for hyperspectral data communication according to Band SeQuential (BSQ) acquisition format in such a way that bands can be collected band by band. By virtue of BSQ users are able to develop Progressive Band Processing (PBP) for hyperspectral imaging algorithms so that data analysts can observe progressive profiles of inter-band changes among bands. Its advantages have been justified in several applications, anomaly detection, constrained energy minimization, automatic target generation process, orthogonal subspace projection, PPI, etc. This paper further extends PBP to FIPPI. The idea to implement PBP-FIPPI is to use two loops specified by skewers and bands to process FIPPI. Depending upon which one is implemented in the outer loop two different versions of PBP-FIPPI can be designed. When the outer loop is iterated band by band, it is called to be called Progressive Band Processing of FIPPI (PBP-FIPPI). When the outer loop is iterated by growing skewers, it is called Progressive Skewer Processing of FIPPI (PSP-FIPPI). Interestingly, both versions provide different insights into the design of FIPPI but produce close results.