  Axion-like particles (ALPs) have been studied in numerous experiments to
search for their interactions, but most studies have focused on deriving bounds
for the single coupling. However, in ultraviolet (UV) models, these couplings
can appear simultaneously, and their interplay could have important
implications for collider and beam dump searches. In this study, we investigate
the concurrent effects of the ALP-photon and ALP-electron couplings in a
simplified model and examine how their simultaneous presence modifies existing
bounds. We find that modifications to production cross-sections, decaying
branching ratios, and the lifetime of the ALP are the major effects. Our
results show that low-energy electron-positron colliders such as Belle-II and
BaBar are primarily affected by the first two factors, while beam dump
experiments such as E137 and NA64 are affected by the cross sections and
lifetime. We also consider two UV models - the KSVZ model and a lepton-specific
version of the DFSZ model - which have only one of the two couplings at
tree-level. However, the other coupling can be generated at loops, and our
analysis reveals that the simultaneous presence of the two couplings can
significantly modify existing bounds on these models for $10^{-3} < m_a < 10$
GeV, especially for beam dump experiments. Overall, our study highlights the
importance of considering the concurrent effects of the ALP-photon and
ALP-electron couplings in future collider and beam dump analyses.
