Unsigned RFA as in a player who's contract was up after last season, not this season, was qualified, but never signed over the course of this year. There are a handful of teams with players in this situation.
With RFA players who's contracts are expiring this year, yes you can qualify as many as you like by submitting a qualifying offer.
Qualifying offer: a 1 year deal that meets the criteria laid out below.
If the players base salary was:
$500,000 - $1.5 million = 110% of previous contract
over $1.5 million - $3 million = 105% of previous contract
over $3 million = 100% of previous contract
Qualifying offers are presented as follows.
Example
Player name qualifying offer - 1 year, $2 million
Anything more than this (ie: long discussion about players role, etc.) is considered the start of a negotiation and would count against the 6 negotiations.