I have been told on very good authority, though, that there is a legal requirement that each set of new pages be taped on both sides to an original page. (Anything anyone is told, no matter how good the authority, can change five minutes after the telling, so I am willing to be corrected.) If that rule is now in effect, it would limit the number of added sets to the number of original pages, minus those at the front used for text - 22 or 46 new sets, depending on whether your original passport had 24 or 48 pages. As a practical matter, a passport would become impractically thick well before this point. Others have posted here that embassies are reluctant to add a fourth new set, up to the point of refusal.