After a lukewarm critical reception in the U.K., “Broadchurch” has finished its second season, with a third already in the planning stages. Yet the griping about the just-concluded arc would seem to say more about the limitations of extending this sort of concept than the execution itself.

The BBC America show’s considerable popularity in the U.K. especially, coupled with a rapturous critical response, made a second season an inevitability. The problem was that the story had come to something approaching a logical and satisfying conclusion, with a solution to the central mystery in the case of who had killed a young boy, triggering shock waves across the small town in which he lived.

Season two sought to address that challenge by extending the first story – through a bitter trial of the killer, which reopened still-fresh wounds – and introducing a second plot, with the tormented inspector Alec Hardy (David Tennant) revisiting an old unsolved case in which he was convinced the perpetrator had gone free.

The series certainly loaded up in terms of casting this time around, with Charlotte Rampling and Marianne Jean-Baptiste as the dueling barristers in the court case – the former her rival’s mentor – while James D’Arcy and Eve Myles played the central couple in the long-simmering murder mystery, which involved the disappearance of two young girls.

As with the first “Broadchurch,” however, the resolution – emotionally shattering as it was in laying the crime on the doorstep of one of the detectives, Ellie Miller (the brilliant Olivia Colman) – felt secondary to the journey and the various red herrings sprinkled along the way. As for the trial, much of the kick for an American audience came from differences in the rules of evidence and judicial discretion in reaching a verdict, while the outcome (and SPOILER ALERT if you haven’t watched) proved sobering but somewhat anticlimactic.

Ultimately, the boy’s killer, Joe Miller (Matthew Gravelle), walked free, but not without consequences, as the town essentially orchestrated an old-fashioned banishing. And if that didn’t bring closure to the boy’s devastated family, it at least spared them from the constant reminder of this miscarriage of justice – or worse, doing something to settle accounts and seek justice on their own that only would have escalated the tragedy.

Taking a (pardon the expression) broader view, “Broadchurch’s” second season underscores the challenge that goes with producing limited series that tell self-contained stories and, in success, introduces the daunting question of how to then keep the franchise alive. In this case, creator Chris Chibnall chose to try splitting the difference between starting over (a la the second seasons of “True Detective” and “Fargo”) and concocting new wrinkles to keep the existing cast together, even if it would have been just as logical for Hardy and Miller (or as he called her, “Miiiiiiiill-er!”) to simply go their separate ways.

In the final analysis, there was still enough to recommend season two to make it enjoyable and worthwhile – certainly compared with the ill-advised U.S. version, “Gracepoint,” which aired between these seasons – although watching it has also somewhat dampened enthusiasm for a third installment. With the benefit of hindsight, the second-guessing that surrounded this second iteration perhaps highlights just how hard it is to thread the needle between returning to “Broadchurch,” the place and those who inhabit it, as opposed to just “Broadchurch” the state of mind.