Question about collisions on multiple voices

[Paolo Prete]

Hello,

given two voices, for example:

\new Staff <<
  \new Voice = "first"
    { \voiceOne c'8[ c'^> c' c']}
  \new Voice= "second"
    { \voiceTwo \stemUp c''8[ c'' c'' c''] }
>>

... is it possible to make the script " ^>"  avoid collisions on the other voice too?

Thanks!