The normal maximum is (7 + Commander Level/10). VIC Status gives a static +2 to your max booster. You can increase your max booster with command points in the efficiency skill tree but not higher than (maxE/25).
The maximum BB is always rounded up to the nearest decimal. If you use a BB that is lower than the maximum, you can only select values rounded to the nearest unit from the dropdwon menu.
It is adviseable to "probe" new targets with 1x BB to avoid losses with max BB as those give you a serious decrease of your maxE. Your best targets which you can reliably beat you want to hit with max BB as to multiply your gains.
The Battle Booster can be switched between 1x BB and Max BB using the toggle switch on the right hand pane, under the chat window.