  Superconducting quantum interference devices (SQUIDs) are among the most
sensitive detectors for out-of-plane magnetic field components. However, due to
their periodic response with short modulation period $M = 1 \Phi_0$, determined
by the magnetic flux quantum $\Phi_0 \approx 2.068\times
10^{-15}\,\mathrm{Wb}$, it is difficult to infer the value of the magnetic flux
unambiguously, especially in case the magnetic flux enclosed in the SQUID loop
changes by many flux quanta. Here, we demonstrate that by introducing a second
degree of freedom in the form of a second SQUID, we substantially enhance the
modulation period $M$ of our device without sacrificing sensitivity. As a proof
of concept, we implement our idea by embedding two asymmetric direct current
SQUIDs into a common tank circuit. By measuring the reflection coefficient of
the device, we extract the two lowest energy eigenfrequencies as a function of
the external magnetic flux created by a superconducting field coil, from which
we experimentally deduce a modulation period $M \geq 15 \Phi_0$, as well as the
magnetic offset-field $B_0 = 22\,\mathrm{nT}$ present in our experiment.
