Here's a four-measure excerpt from an arrangement for violin (by Maxim Jacobsen). There are points in the score – two indicated in red here – where there are three slurs in effect simultaneously.
The violin bow only goes in one direction at a time! So what is the writer trying to convey with these? How would the meaning change if only the longest slur were written over those segments?
The first arrow is tying into the eighth note. The quarter notes at the beginning of the phrases indicate a three count, at D, D, DE in the first bar, so the sixteenth notes would be a sextuplet run, tying the last note of the second sextuplet into the eighth note. I suspect that the last two eighth notes would be played Portato, separating the notes with the same bow direction. Basically some fast arpeggio runs over the top of the quarter and eighth notes.
Since the quarter notes are independently beamed I suspect that the note might be held in a double stop while playing the quick run.
Slurs are ambiguous: they may mean ties between note heads (notational convention), bow direction (technical instruction), or phrasing (musical expression). There's no particular reason why all three couldn't be in effect at some point.
First, I view the ties above the notes (last beat and a half of the measures) as a phrasing indicator, to ensure you lead the final triplet into the last beat smoothly.
Next, I suspect the composer wants you to maintain the initial note (the down-stem quarter notes) thru the beat as a "drone" under the triplets. So, double-stops.
Finally, the tie between the final note of the triplet and the first note of the third beat is to emphasize that there should be no re-attacking of any kind there.
