One should remember that 'length', 'mass' and 'capacity' are the base standards of the commercial systems, where 'capacity' is volume measured by bulk comparison, eg pouring or weighing.
NASA, for example, used the inch-pound-second system, since these are the base units defined in US legislation. The unit of 'slinch' (ie 386 lb = ips slug), has been observed, along with a measure of a slinch-mole (written as (lb-g-s^2/in)-mole ).
The scientific systems are essentially selected from length and mass, along with a time unit. There really is no need to follow the legal standard, except you might run into legal problems down the track.
The number of base units depends on the number of free variables you would have in a system. The size of the units do not change with dimension, this is because the dimension is relative to a body of equations, which define X quantities in (X-B) equations. The B remaining quantities are defined in the preamble.
For example, the mole was a derived unit, essentially "mass/daltons". The daltons were found from the chemical tables, and divided into mass, to give mass-mole. This is a derived unit, with dimensions M.
In SI, the coherent unit is not 'dalton' but 'kilodalton', so the unit mole is actually 'kilogram / kilodalton', but the tables still show the weights in daltons. So there is an additional constant in the CODATA tables that gives kilodaltons. (ie 1 kg/dalton = 1000 moles)
Were one to construct base units that actually meant something to science, then the choice would be something like density, velocity, time. Density is something that really is constant from atoms to stars. Velocity is consistant with the thermal state of things. Size is then dependent on the appropriate power of time. In SI, replacing time with 10^-9 seconds, would pretty much eliminate all of the exponents in the CODATA atomic values, and with t=10^-12, v=10^3 (ie thermal velocities), nearly all exponents disappear.
The correct approach to dimensions is to simply regard them as algebraic blobs, which can be multiplied, divided etc. Note that any given system does not have a full set of dimensions, and a full set would make the mathematics unwealdy. None the same, Leo Young in 1961, showed a set of equations, to which the cgs-gaussian, and SI were both coherent to, by supposing two additional base units assumed different values in the different systems.