  We carry out extended symmetry analysis of the (1+2)-dimensional
Boiti-Leon-Pempinelli system, which enhances and generalizes many results
existing in the literature. The complete point-symmetry group of this system is
computed using an original megaideal-based version of the algebraic method. A
number of meticulously selected differential constraints allow us to construct
families of exact solutions of this system, which are significantly larger than
all known ones. After classifying one- and two-dimensional subalgebras of the
entire (infinite-dimensional) maximal Lie invariance algebra of this system, we
study only its essential Lie reductions, which give solutions beyond the above
solution families. Among reductions of the Boiti-Leon-Pempinelli system via
differential constraints or Lie symmetries, we identify a number of famous
partial and ordinary differential equations. We also show how all the
constructed solution families can significantly be extended using Laplace and
Darboux transformations.
