The relevance of image schemas in metaphoric extension has been long highlighted in Cognitive Linguistics literature. The image-schematic makeup of a metaphoric source is preserved in the target, in a way consistent with the structure of the latter (Lakoff, 1993). More recently, Sullivan (2013) has raised a similar case for semantic frames, in a constructional framework. Metaphoric mappings are licensed only if the semantic frame of the source is compatible with the conceptual metaphor profiled by the target. The present work integrates Sullivan and Lakoff's approach to invariance, on the basis of the following hypothesis: the compatibility between a semantic frame evoked by a lexical construction and a conceptual metaphor is susceptible to an image-schematic blueprint, already present in the etymologically prior meaning of the construction. Thus, invariance is hypothesised to hold across categorisation levels of different schematicity, but also across time. The case study re-takes the analysis of the adjectival terms brilliant, sunny and bright, under the generalised invariance hypothesis. The metaphorical potential of a term is shown to be at the same time constrained as well as motivated by this strong version of invariance.