You can sign a solid backup for less then around 1-2M i would not worry about it and they will likely give Jimenez a chance to win in in spring anyway so they won't break the bank on a backup.
As for the bullpen i have always been a big believer that you don't throw big bucks around in the pen especially when you have 3 solid pieces in there as is (Osuna, Grilli, Big Joe). Logan/Blevins might command 7 per year and that would be the biggest guy i would go after.