I got lucky once in that situation. Had no space left and travelled to Japan. Check-in personnel did not check if passport had space. At immigration, the officer flipped all the pages, sighed, looked puzzled, looked at me … and without me having to beg, decided to place the stick horizontally and partially covering another stamp in one of the pages.

I then went on to Singapore, where I got scolded by suggesting the immigration officer he could stamp on page number “x”. It would fit, tightly, but fit. The officer took personal offense, raised his voice, and said I would not be allowed in. I was very nice throughout all the process, apologized, mentioned the passport issuing authority in my country was shut down for the lack of official passport paper (which was true). He then sent me to a separate room, where another officer asked me 10,000 questions, after which he stamped me in. Exactly were I had suggested the other officer could stamp …

In Singapore, I was able to contact my Embassy. Explained the situation, also got kind of lectured by them, but was able to issue a new passport in the following day.

Not a comfortable situation …