Alex is inviting 84 * 2 / 3 = <<84*2/3=56>>56 guests.
Bridgette and Alex’s guests will need 84 + 56 = <<84+56=140>>140 plates.
The caterer makes 10 extra plates, so they will need 140 + 10 = <<140+10=150>>150 plates.
To put 8 asparagus spears on each plate, the caterer will need 150 * 8 = <<150*8=1200>>1200 asparagus spears.
#### 1200