Several studies on heritage language (HL) acquisition investigate a single linguistic structure, showing how language exposure or cross-linguistic effects affect its acquisition. Here, we consider HL speaking children's mastery of several linguistic structures using a cloze-test. We examine how their language competence is affected by language exposure variables and age. We tested 180 children between the ages of 8 and 16, living in Switzerland and speaking European Portuguese as HL and French, German or Italian as their societal language. The items of the cloze-test cluster around two levels of difficulty, with the items at the second level corresponding to structures that are acquired late in Portuguese monolingual acquisition. Older age and a greater amount of formal instruction in the HL lead to better performance. The role of the amount of formal instruction varies based on the level of difficulty of the target structures. Cross-linguistic influence does not affect the results.