[gleeman]

How would you test is the acid in question triprotic experimentally? 

I have been thinking of titrating the acid first with NaOH and checking the endpoint.
I think that there are some differences in the substances formed depending on the amount of hydrogens.

The  reactions known are the following:

    H3PO4(s)   + H2O(l) ⇌ H3O+(aq) + H2PO4–(aq)       Ka1= 7.5×10−3

    H2PO4–(aq)+ H2O(l) ⇌ H3O+(aq) + HPO42–(aq)       Ka2= 6.2×10−8

    HPO42–(aq)+ H2O(l) ⇌ H3O+(aq) +  PO43–(aq)        Ka3= 2.14×10−13

But above all, is it possible to test the type of acid through the titration with strong base NaOH?

[IITian]

Not quite sure.

Judging the end point of titration involving weak acid and a strong base is tricky.

[Borek]

Only two endpoints visible when titrating in water.

You should check mass of chemical equivalents in different reactions or determine molar mass using some other method.