I was booking by phone with LY in TLV for 4 family members.
On their website I saw a specific price. When I called I was quoted higher price. I told the agent that I just saw a cheaper price on their website for same flights. She said: yes, but not for 4 seats, on the return there is only 1 seat left in T-class. I told her that I will book if she can get 4 seats at the cheaper price (with T-class on the return).
She went to a supervisor and came back with approval.
So- if you need more seats for Same reservation than available at a cheap fare-class, it can be "arranged".
By the way, I called it "Fare Grabbing", is there a more appropriate name?