Things that can impact blow-off:
1. Inadequate head space: If the there isn't room for krausen formation between the beer and the top of the fermentor, it will come out of the airlock.
2. Fermentation is too vigorous: Very high gravity beers or too high of a fermentation temperature will create excessive krausen/foaming.
I usually use a blow-off tube during active fermentation (first 3-4 days) because they are less maintenance (usually don't need to be refilled or cleaned), then switch to a three-piece airlock.
I wouldn't recommend agitating the fermentation vessel, there's no reason to mobilize the krausen. It will just fall back down and dissolve or turn into sediment. No need to skim it off either. Agitation will just increase blow-off. Also, given how vigorous the fermentation is, oxygen is being actively purged so swapping out the airlock or switching to a tube is not a risky move.