The search for extensions to GR, has prompted the developments of many potential options which, to varying degrees, have been studied and confronted with observations in special regimes --typically linear ones with respect to rather 'simple' scenarios. Gravitational wave astronomy provides the opportunity to confront them in a much richer and complex regime which unearths significant roadblocks that obstruct the definition and/or study of consequences of many of such extensions. This talk will review some of these problems, illustrate consequences and discuss a potential way through for studying the potential role such extensions might have in the strongly gravitating/non-linear regime. [please email a.held@imperial.ac.uk for zoom link or password]