  Gravitational waves have been instrumental in providing deep insights into
the nature of gravity. Next-generation detectors, such as the Einstein
Telescope, are predicted to have a higher detection rate given the increased
sensitivity and lower cut-off frequency. However, this increased sensitivity
raises challenges concerning parameter estimation due to the foreseeable
overlap of signals from multiple sources. Overlapping signals (OSs), if not
properly identified, may introduce biases in estimating post-Newtonian (PN)
coefficients in parameterized tests of general relativity (GR). We investigate
how OSs affect $-1$PN to 2PN terms in parameterized GR tests, examining their
potential to falsely suggest GR deviations. We estimate the prevalence of such
misleading signals in next-generation detectors, and their collective influence
on GR tests. We compare the effects of OSs on coefficients at different PN
orders, concluding that overall the 1PN coefficient suffers the most. Our
findings also reveal that while a non-negligible portion of OSs exhibit biases
in PN coefficients that might individually prefer to conclude deviations from
GR, collectively, the direction to deviate is random and a statistical
combination will still be in favor of GR.
