  Finite volume schemes often have difficulties to resolve the low Mach number
(incompressible) limit of the Euler equations. Incompressibility is only
non-trivial in multiple spatial dimensions. Low Mach fixes, however generally
are applied to the one-dimensional method and the method is then used in a
dimensionally split way. This often reduces its stability. Here, it is
suggested to keep the one-dimensional method as it is, and only to extend it to
multiple dimensions in a particular, all-speed way. This strategy is found to
lead to much more stable numerical methods. Apart from the conceptually
pleasing property of modifying the scheme only when it becomes necessary, the
multi-dimensional all-speed extension also does not include any free parameters
or arbitrary functions, which generally are difficult to choose, or might be
problem dependent. The strategy is exemplified on a Lagrange Projection method
and on a relaxation solver.
