  The envelope theory is a method to easily obtain approximate, but reliable,
solutions for some quantum many-body problems. Quite general Hamiltonians can
be considered for systems composed of an arbitrary number of different
particles in $D$ dimensions. In the case of identical particles, a compact set
of 3 equations can be written to find the eigensolutions. This set provides
also a nice interpretation and a starting point to improve the method. It is
shown here that a similar set of 7 equations can be determined for a system
containing an arbitrary number of two different particles.
