Past kinetic simulations and spacecraft observations have shown that traveling foreshocks (TFs) are bounded by either foreshock compressional boundaries (FCBs) or foreshock bubbles (FBs). Here we present four TFs with a different kind of structure appearing at one of their edges. Two of them, observed by the Cluster mission, are bounded by a hot flow anomaly (HFA). In one case, the HFA was observed only by the spacecraft closest to the bow shock, while the other three probes observed an FCB. In addition, two other TFs were observed by the MMS spacecraft to be delimited by a structure that we call HFA-like FCB. In the spacecraft data, these structures present signatures similar to those of HFAs: dips in magnetic field magnitude and solar wind density, decelerated and deflected plasma flow and increased temperature. However, a detailed inspection of these events reveals the absence of heating of the SW beam. Instead, the beam almost disappears inside these events and the plasma moments are strongly influenced by the suprathermal particles. We suggest that HFA-like FCBs are related to the evolution and structure of the directional discontinuities of the interplanetary magnetic field whose thickness is larger than the gyroradius of suprathermal ions. We also show that individual TFs may appear together with several different types of transient upstream mesoscale structures, which brings up a question about their combined effect on regions downstream of the bow shock.