Acid solution — lower pH when diluted
You run into all sorts of problems when the pH is outside of the range of 1 to 13. For example, in Environ. Sci. Technol. (2000) 342, p. 254-258, they say:


  [...] the former National Bureau of Standards (NBS) established a set of conventions that limits measurements to 1 &lt; pH &lt; 13 and to ionic strength, I &lt; 0.1. The main limitations are the activity coefficient expression, the range of defined standard pH buffers, and interferences with the reversible response of the glass H+-sensitive membrane electrode.


They go on to use standard of concentrated sulfuric acid to define the pH, using a Pitzer model to predict activity coefficients (figure from researchgate) :




  In reality it is completely opposite. So what is the catch?


If you do the math, the extreme pH of -5 shown in the figure corresponds to a hydrogen ion activity of hundred-thousand. The concentration of water for pure water is "only" ~55 mol/L, so this must reflect an activity coefficient far from one.