Multilingual pre-trained language models (PLMs) have demonstrated impressive performance on several downstream tasks on both high-resourced and low-resourced languages. However, there is still a large performance drop for languages unseen during pre-training, especially African languages. One of the most effective approaches to adapt to a new language is language adaptive fine-tuning (LAFT) — fine-tuning a multilingual PLM on monolingual texts using the pre-training objective. However, African languages with large monolingual texts are few, and adapting to each of them individually takes large disk space and limits the cross-lingual transfer abilities of the resulting models because they have been specialized for a single language. In this paper, we perform multilingual adaptive fine-tuning (MAFT) on 17 most-resourced African languages and three other high-resource languages widely spoken on the continent – English, French, and Arabic to encourage cross-lingual transfer learning. Additionally, to further specialize the multilingual PLM, we removed vocabulary tokens from the embedding layer that corresponds to non-African writing scripts before MAFT, thus reducing the model size by 50%. Our evaluation on two multilingual PLMs (AfriBERTa and XLM-R) and three NLP tasks (NER, news topic classification, and sentiment classification) shows that our approach is competitive to applying LAFT on individual languages while requiring significantly less disk space.