  The multilevel field-antifield formalism is constructed in a geometrically
covariant way without imposing the unimodularity conditions on the hypergauge
functions. Thus the previously given version [1,2] is extended to cover the
most general case of Lagrangian surface bases. It is shown that the extra
measure factors, required to enter the gauge-independent functional integrals,
can be included naturally into the multilevel scheme by modifying the boundary
conditions to the quantum master equation.
