Could a Scandinavian language be developed that is mutually intelligable to all four?

I was first intrigued by this prospect when I was in high school and a girl from Upsalla, Sweden and a girl from Oslo, Norway were conversing – in which language I do not know.

They wrote down some lengthy word lists for me, and a girl from Denmark also added their words, Whereas there were some differences, the similarities were greater. As an adult, exchange students I have known have continued to express that the languages are different.

There are two dialects or versions of the Norwegian language, and then there is Swedish and Danish. Four languages. It is said that someone who learns Norwegian can comprehend written Danish and spoken Swedish moderately well. Finnish is a Baltic language and not Scandinavian; Icelandic is a far older language than the other Scandinavian languages.

To this untrained English speaker, I can see far more similarities than differences in the two Norwegian languages or dialects, spoken Swedish and written Danish. And, as an English speaker, I see our own English language as containing many variables, alternate words, dialects, foreign words, and loan words.

Whereas no single Scandinavian language is completely understood by all the others, how difficult would it be to develop a mutually understandable Scandinavian language?