  Strong gravitational lensing can provide accurate measurements of the stellar
mass-to-light ratio $\Upsilon$ in low-redshift ($z$ $\lesssim$ 0.05) early-type
galaxies, and hence probe for possible variations in the stellar initial mass
function (IMF). However, true multiple imaging lens systems are rare, hindering
the construction of large nearby lens samples. Here, we present a method to
derive upper limits on $\Upsilon$ in galaxies with single close-projected
background sources, where no counter-image is detected, down to some relative
flux limit. We present a proof-of-principle application to three galaxies with
integral field observations from different instruments. In our first case
study, only a weak constraint on $\Upsilon$ is obtained. In the second, the
absence of a detectable counter-image excludes stellar masses higher than
expected for a Salpeter IMF. In the third system, the current observations do
not yield a useful limit, but our analysis indicates that deeper observations
should reveal a counter-image if the stellar mass is any larger than expected
for a Milky Way IMF. We discuss how our method can help enlarge the current
samples of low-$z$ galaxies with lensing constraints, both by adding upper
limits on $\Upsilon$ and by guiding follow-up of promising single-image systems
in search of fainter counter-images.
