If "mia" is proper, can the form "mien" also be used for direction as an equivalent to "min"?

Donu ĝin al ŝi -> Donu ĝin ŝin -> Donu ĝin ŝien.

La hundo kuris al li -> La hundo kuris lin -> La hundo kuris lien.

I ask this based on kie/kien, ekstere/eksteren, ktp.
It could improve my sentence flow, but I wonder whether if it would be understood or seen as grammatically correct.

Thank you for your answers to my question.

I'm afraid not. I thought about that too when I had first started getting into word building. Though it might be a logical construction to say "Mi donis lien la pilkon" (= "I gave him the ball" ), pronouns usually don't get used like that in word building. Think of them as exceptions, words with a special meaning. Maybe it's even gramatically correct, I'm not sure, but I've never seen that form used nor in a dictionary.

If it's any consolation, that form wouldn't really affect how quickly or concisely you speak Esperanto, because "al mi" and "mie" both have two syllables anyway.

The pronouns are "oddballs" in the sense that the normal grammatical vowel endings are never applied to them (with the exception of -a, but this is not a true adjectival ending, rather a possessive). This probably has a lot to do with the influence of Indo-European languages.