  The detection of a gravitational capture of a stellar-mass compact object by
a massive black hole (MBH) will allow us to test gravity in the strong regime.
These sources form via two-body relaxation, by exchanging energy and angular
momentum, and inspiral in a slow, progressive way down to the final merger. The
range of frequencies is localised in the range of millihertz in the case of MBH
of masses $\sim 10^6\,M_{\odot}$, i.e. that of space-borne gravitational-wave
observatories such as LISA. In this article I show that, depending on their
orbital parameters, intermediate-mass ratios (IMRIs) of MBH of masses between a
hundred and a few thousand have frequencies that make them detectable (i) with
ground-based observatories, or (ii) with both LISA and ground-based ones such
as advanced LIGO/Virgo and third generation ones, with ET as an example. The
binaries have a signal-to-noise ratio large enough to ensure detection. More
extreme values in their orbital parameters correspond to systems detectable
only with ground-based detectors and enter the LIGO/Virgo band in particular in
many different harmonics for masses up to some $2000,\,M_{\odot}$. I show that
environmental effects are negligible, so that the source should not have this
kind of complication. The accumulated phase-shift is measurable with LISA and
ET, and for some cases also with LIGO, so that it is possible to recover
information about the eccentricity and formation scenario. For IMRIs with a
total mass $\lessapprox 2000\,M_{\odot}$ and initial eccentricities up to
$0.999$, LISA can give a warning to ground-based detectors with enough time in
advance and seconds of precision. The possibility of detecting IMRIs from the
ground alone or combined with space-borne observatories opens new possibilities
for gravitational wave astronomy.
