  The current SI second based on the atomic hyperfine transition in the ground
state of 133Cs is expected to be replaced by a new definition based on optical
frequency standards, whose estimated uncertainty has now been established two
orders of magnitude lower than the accuracy of the best Cs primary standards.
However, such a redefinition of the second is hindered by the fact that many
atomic species are potential contenders to become the new primary frequency
standard. In this paper, we propose to resolve this issue by defining a
composite frequency unit based on the weighted geometric mean of the individual
frequencies of different atomic transitions. This unit has the property to be
realisable with any single clock whose transition composes the unit, provided
that at least a few frequency ratios are available, with an accuracy that
marginally differs from the nominal clock uncertainty. We show that the unit
can be updated as the performances of the contributing transitions evolve,
without incurring a drift on the unit itself.
