In your current campaign or adventure, assuming there is one, what is the villain or antagonist(s) doing? What's their plan? How are they enacting it? Do they have a contingency in case a motley crew of troublemakers sticks their collective nose where it doesn't belong? What happens if no one stops them and they succeed?
I run multiple groups and a pretty hardcore sandbox. I don't always have a single BBEG; the campaign has a bunch of bad guys in the background, and the pcs sometimes engage with some of them, while at other times, the bad guys become setting details. Also, the Alpha group (who are high to epic level) just dealt with an apocalyptic event that included defeating Ygorl, the slaad lord, who was basically serving as an avatar of Chaos. They defeated him maybe three games ago.
With that said:
Team Alpha just defeated another of their main adversaries, the Dread Emperor, over the last couple of sessions, along with their former ally turned foe out of duty (the DE was the rightful liege of the former ally). Their overall "BBEG" is Chaos, which they have already dealt massive setbacks to, but which isn't currently represented by a particular individual (that they are aware of).
Team Beta- the orc group doesn't have a current villain lined up. They just finished an adventure that gave them a prophecy that they're trying to follow involving becoming parents of the children of the gods.
Team Beta- the ghost wagon group just slew a dragon that was collecting baby dragons in a bid to become an exarch of Tiamat. No current bad guy lined up, but the looming menace is their transportation, the so-called ghost wagon, which seems malevolent, may be sentient, and draws spirits to it.
Team Gamma hasn't started yet, but is going to follow a pc paladin as he recruits a group of good pcs to go on a quest to three different material worlds- basically, Gamma World, Star Trek, and a super low magic fantasy world called Arba- to retrieve the Crown, Orb, and Scepter of Good Might. No overarching bad guy, but there will be adversaries in all three settings, and it's possible some demon or devil or other Evil power will try to interfere if they become aware of the party's actions.
Team Delta is kind of the exception to the rest. They have several BBEGs, but they don't realize it (I don't think). First, two old enemies have joined forces and are out to kill them. Second, they don't know it, but they have just picked up an artifact that will lead them into conflict with its traditional foe, Master Control, an entity composed of information that, in my campaign, is responsible for the clockwork horrors and many, many variants.
So the two old enemies are a dao and a cambion. They have each been bested by the pcs and both hold a grudge. After meeting and learning they had the pcs in common, the two have begun trying to kill the pcs, starting with an assassin imp that struck when the pcs were in a combat. They'll be stepping it up in the future. Since they're on other planes, they are both hard to reach and well-guarded.
Master Control is a whole nother matter. From its perspective, the problem that prevents the world from achieving its proper balance is civilization. Civilization is caused by intelligence, so the clear answer is to eliminate intelligence. To that end, it seeks to build large towers that will release gas that don't affect the current generation, but ensure that their offspring are born with an intelligence no higher than 2. This has been going on in secret for years, although several pcs have come across such low-intelligence humans, though none have caught on that they're a sign of something very important and very dangerous.
Once MC becomes aware that the artifact is active, it will have to thread the needle between revealing its presence and taking the artifact out of play.