We present the MULTISEM systems submitted to SemEval 2020 Task 3: Graded Word Similarity in Context (GWSC). We experiment with injecting semantic knowledge into pre-trained BERT models through fine-tuning on lexical semantic tasks related to GWSC. We use existing semantically annotated datasets and propose to approximate similarity through automatically generated lexical substitutes in context. We participate in both GWSC subtasks and address two languages, English and Finnish. Our best English models occupy the third and fourth positions in the ranking for the two subtasks. Performance is lower for the Finnish models which are mid-ranked in the respective subtasks, highlighting the important role of data availability for fine-tuning.