Of terms formed by prefixes trans-, pan-, inter- attached to base galactic, only intergalactic ("Occurring between galaxies") unequivocally denotes involvement of multiple galaxies.
From wiktionary links in previous paragraph, trans- indicates "across, through, over, beyond, to or on the other side of, outside of". One of the most common uses of trans- is to denote "across the whole of", as in transcontinental ("Crossing, spanning a continent") and in the name Trans Global Highway ("a range of proposed highway systems that would link all six of the seven inhabited continents on Earth"). Following those examples, trans-galactic would mean "spanning the galaxy", involving one galaxy rather than several.
Prefix pan- is "A combining form meaning 'all'". For example, Pan-Asian means "Covering or representing all of Asia" and Pan-American "Covering or representing all of the Americas (both North America and South America), particularly with respect to events involving representatives of most or all countries in the Americas". Following those terms I am more inclined to interpret pan-galactic as "all of the galaxy" or "all the stars of the galaxy" rather than as "all the galaxies".
Prefix inter- indicates "among, between, amid, during, within, mutual, reciprocal". Examples include intercontinental ("Taking place between two or more continent") and interstellar ("between the stars" or "among the stars") and intergalactic ("Occurring between galaxies").
Also consider term multi-galactic; prefix multi- indicates "Resembling, pertaining to many or many things".