The intermediate- to high-mass star-forming region IRAS 20343+4129 is an excellent laboratory to study the influence of high- and intermediate-mass young stellar objects on nearby starless dense cores, and investigate for possible implications in the clustered star formation process. We present 3 mm observations of continuum and rotational transitions of several molecular species (C2H, c-C3H2, N2H+, NH2D) obtained with the Combined Array for Research in Millimetre-wave Astronomy, as well as 1.3 cm continuum and NH3 observations carried out with the Very Large Array, to reveal the properties of the dense gas. We confirm undoubtedly previous claims of an expanding cavity created by an ultracompact H ii region associated with a young B2 zero-age main sequence (ZAMS) star. The dense gas surrounding the cavity is distributed in a filament that seems squeezed in between the cavity and a collimated outflow associated with an intermediate-mass protostar. We have identified 5 mm continuum condensations in the filament. All of them show column densities consistent with potentially being the birthplace of intermediate- to high-mass objects. These cores appear different from those observed in low-mass clustered environments in several observational aspects (kinematics, temperature, chemical gradients), indicating a strong influence of the most massive and evolved members of the protocluster. We suggest a possible scenario in which the B2 ZAMS star driving the cavity has compressed the surrounding gas, perturbed its properties and induced the star formation in its immediate surroundings.