@”Kapitán Denis” Making another Slavic mandatory in schools would help more I think. From personal experience, knowing two Slavic languages from different groups (South and West in my case) helps in many ways with understanding other Slavic languages. E.g. I understand Slovenian much better than my compatriots, when I was in contact with Ukrainian I understood it better than people around me etc. I have a feeling that if I knew another one from Eastern group I could have basic communication with any Slavic speaker.
Then again our institutions could work together over longer period of time to bring closer our vocabularies. You have a lot of terms that exist in all Slavic languages but are considered archaic by some, we could restore those which fell out of use, especially those replaced with foreign expressions.