Where do aspectual variants of light verb constructions belong?

Expressions with an aspectual variant of a light verb, e.g. 'take on debt' vs. 'have debt', are frequent in texts but often difficult to classify between verbal idioms, light verb constructions or compositional phrases. We investigate the properties of such expressions with a disputed membership and propose a selection of features that determine more satisfactory boundaries between the three categories in this zone, assigning the expressions to one of them.