We show that the multi-boson KP hierarchies possess a class of discret
e symmetries linking them to discrete Toda systems. These discrete sym
metries are generated by the similarity transformation of the correspo
nding Lax operator. This establishes a canonical nature of the discret
e transformations. The spectral equation, which defines both the latti
ce system and the corresponding Lax operator, plays a key role in dete
rmining pertinent symmetry structure. We also introduce the concept of
the square root lattice leading to a family of new pseudo-differentia
l operators with covariance under additional Backlund transformations.