Pepsin digests proteins, as we know, but can it digest other enzymes that are actually made up of proteins, like digesting other pepsin molecules?
Pepsin does cleave itself (Ingram, 1951) - this is termed autolysis. Pepsin (and other proteases) act on proteins with the right amino acid sequences. Pepsin prefers to cleave at phenylalanine, tryptophan or tyrosine residues (Lehninger, A. Principles of Biochemistry).
* Pepsin can also cleave inactive 'zymogen' enzymes to activate them. One of these zymogens is pepsinogen (an inactive form of pepsin itself). So you could argue that pepsin is cleaving itself here but I personally wouldn't, since pepsinogen isn't really pepsin.