After the normal possibilities of this module are exhausted, you might wish to continue to center the action of your campaign around the KEEP by making it the base for further adventures which you may devise. For example (assuming that the group has done good service for the Castellan), have a large force of bandits move into the area, and then appoint the group to command an expedition of KEEP troops, mercenaries, and so on to drive them away. Or the party might become "traders" operating out of the KEEP. hoping to find adventures as they travel in the surrounding area.
The Keep on the Borderlands
I'm not certain that anyone has described their PCs becoming "traders" operating out of the Keep, although the trade routes and merchant class detailed in GAZ 11 "The Republic of Darokin" would be very useful, for such a campaign.
Return to the Keep on the Borderlands:
Cover to "Return to the Keep on the Borderlands" (1999) by John D. Rateliff. Illustration by Fred Fields.
"Return to the Keep on the Borderlands" for AD&D 2e was published as part of the 25th anniversary of the D&D game. The module takes place twenty years after the original adventure. See this post, for the author's retrospective (and Easter eggs).
The NPCs in the Keep, encounters in the Wilderness, and the Caves of Chaos are detailed and well-developed. Rateliff pursued his own ideas with respect to the history of the Keep, and the nature of the Shrine of Evil Chaos, but there's plenty to steal from.
A 16-page mini-adventure by Jeff Grubb, called IQ3 "Warriors of the Gray Queen", was included with InQuest Gamer magazine #50 (June, 1999) as a prelude to "Return to the Keep on the Borderlands". The PCs encounter a caravan, and explore a small dungeon.
An RPGA Adventurer's Guild Adventure by Ed Stark, called "The Displaced" (1999) takes place as the PCs are passing through the hamlet of Riversford on their way to the Keep. "The Displaced" are a family whose homestead has been overtaken by humanoid raiders.
Reclaiming the Caves on the Borderlands:
Cover to SG9 "Reclaiming the Caves on the Borderlands" (2015) by Roderic Waibel. Illustration by Eric Lofgren.
"Reclaiming the Caves on the Borderlands" for 5e provides an interesting take for a sequel. Players use humanoid PCs in an effort to reclaim the Caves of Chaos, a year after events in the original module (which is required to run the scenario).
The text is presented in a B1-format, where individual caves need to be stocked. For those running a BECMI campaign, GAZ 10 "Orcs of Thar" would serve as a useful source of additional material, and is highly recommended.
B2 Beyond the Caves of Chaos:
Cover to B2 "Beyond the Caves of Chaos" (2019) by Bill Barsh. Illustration by Lloyd Metcalf.
"Beyond the Caves of Chaos" for OSRIC/5e provides an answer for what lies beyond the boulder-filled passageway in the Caves of Chaos, something grander and wholly different from a mere passageway to the "Cave of the Unknown".
The adventure is set on the Isle of the Star Witch in Wee Warriors/Pacesetter’s Misty Isles campaign setting, and can serve as a link to other adventures, deeper still (the Underdark of module D1 "Descent into the Depths of the Earth", for example).
B2.5 Blizzard on the Borderland:
Cover to B2.5 "Blizzard on the Borderland" (2019) by Bill Barsh. Illustration by Stefan Poag
"Blizzard on the Borderland" for OSRIC/1e serves as a true sequel to module B2 "The Keep on the Borderlands", designed to be run once the PCs have finished exploring the Caves of Chaos, and neutralized the threat of a humanoid invasion.
The 16-page adventure is designed for 8 characters of levels 2-3, and involves an assault on the Keep in the middle of a snowy blizzard. I've not run it, but it certainly serves a niche for options once possibilities in the original module have been exhausted.