Four Person Presidential Race?

Michael Bloomberg has declined entering the Presidential race because he felt that his candidacy would throw the election to Trump.

But what if Bloomberg knew that if he entered the race, so would another independent candidate, a conservative one?

Could Bloomberg be swayed to enter the race if he knew that a candidate like Rick Perry would run as an independent conservative? I could not see an independent conservative winning a three way race with Trump and Hillary but a four-man race would be winnable, or at the very least throw the election to the House of Representatives.