I get 3 without really trying.
Cavalier 1/Paladin (Holy Tactician, Holy Guide) 5 (These are out of Advanced Class Guide)
First level cavalier gets Tactician: get a bonus teamwork feat and can share that feat with allies for 3 rounds + 1 round/2 levels.
At 3rd level, the Holy Tactician trades aura of courage for "Battlefield Presence", and can grant allies any teamwork feat she possesses with no clear time limit.
At 5th level, the Holy Guide gets the functional equivalent of the cavalier's Tactician ability.
So Holy Guide fires up Teamwork feat #1 at the beginning of the day and keeps it going.
When combat starts, Holy Guide fires up Teamwork feat #2.
Round 2, Cavalier fires up Tactician.
For 3+ rounds, everyone has 2 teamwork feats. For at least 2 rounds, everyone has 3. (You can extend that by taking more levels in either class, of course.)
There are archetypes of other classes that get the tactician ability, too, but most of them pick it up at 4th or 5th level. Also, paladin is the only class I know of with two stacking archetypes with this ability.
(I have a Brawler 1/Holy Tactician-Holy Guide 2. Next level I'll be able to learn a teamwork feats as a move action and pass them out to everyone...There are only a few teamwork feats that are also classed as "combat" feats, but there were enough to make the Brawler dip worth it for me.)
