Among the variety of possible SM extensions, LHC searches pick selected models, often simplified models to guide the searches. The implicit hope is that with this procedure we cover all the reasonable new physics signatures. But this may not be the case. I will show some examples of well-motivated models with additional gauge bosons where one might near-miss the new physics signals in current searches. Or where experiments might find apparently contradictory results in searches apparently equivalent. For example, where mass peaks might be located at different places in ATLAS and CMS.
On a more experimental ground, I will discuss the results in diboson resonance searches, where 7 anomalies or so appear at the 3 sigma level. This fact suggests that the above discussion and examples may be not only academic, but of relevance for actual experiments, and call for more generic searches than the current ones.