Even after adding Benoit and free-agent pitcher Josh Johnson, and making a trade for outfielder Seth Smith, the Padres might not be finished.
Byrnes said late Tuesday that more moves could come.
The Padres aren't adverse to adding a left-handed reliever, even though they picked up one during last week's Rule 5 Draft in Patrick Schuster, who hasn't pitched higher than Class A.
"We're still in touch with several scenarios with left-handed relievers ... probably more through trade than free agent at this point," Byrnes said.
Byrnes also talked about "shuffling out depth," which could mean parting with players projected to be on the 25-man roster or on the bubble of making the Opening Day roster.
That could mean that players like outfielder/first baseman Kyle Blanks and Jesus Guzman could be trade chips either on a singular basis or part of a larger deal.
"We're talking about guys that are in an area of surplus, trading them for depth that can better serve us," Byrnes said.
The Padres would love to add more position players to the upper levels of their Minor League system. And while open to any conversations regarding trades, the team won't move prospects Matt Wisler or catcher Austin Hedges, even though they have been frequently asked about them.
Could something happen this week?
"There's still one or two big ideas still out there, we're not closing the door on anything," Byrnes said.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.