Presently, the largest sample of galaxy clusters selected in X-rays comes from the ROSAT All-Sky Survey (RASS). Although there have been many interesting clusters discovered with the RASS data, the broad point spread function of the ROSAT satellite limits the attainable amount of spatial information for the detected objects. This leads to the discovery of new cluster features when a re-observation is performed with higher-resolution X-ray satellites. Here we present the results from XMM-Newton observations of three clusters: RXC J2306.6−1319, ZwCl 1665, and RXC J0034.6−0208, for which the observations reveal a double or triple system of extended components. These clusters belong to the extremely expanded HIghest X-ray FLUx Galaxy Cluster Sample (eeHIFLUGCS), which is a flux-limited cluster sample (f_{X, 500} ≥ 5 × 10⁻¹² erg s⁻¹ cm⁻² in the 0.1−2.4 keV energy band). For each structure in each cluster, we determine the redshift with the X-ray spectrum and find that the components are not part of the same cluster. This is confirmed by an optical spectroscopic analysis of the galaxy members. Therefore, the total number of clusters is actually seven, rather than three. We derive global cluster properties of each extended component. We compare the measured properties to lower-redshift group samples, and find a good agreement. Our flux measurements reveal that only one component of the ZwCl 1665 cluster has a flux above the eeHIFLUGCS limit, while the other clusters will no longer be part of the sample. These examples demonstrate that cluster–cluster projections can bias X-ray cluster catalogues and that with high-resolution X-ray follow-up this bias can be corrected.