When Q.S.I. first invested in P.S.G. in 2011, its stated aim — according to Khelaifi himself — was to win the French championship “for the next three years” and to become “competitive” in the Champions League.

By most measures, that has been accomplished. Although Monaco won Ligue 1 last year, P.S.G. had picked up the four previous championships. And while P.S.G. was spectacularly eliminated by a Neymar-inspired Barcelona in the round of 16 of the Champions League in March, it had become a fixture in the quarterfinals in the years before that.

It wanted to go further, of course. “Our aim is to make the club an institution respected around the world,” Khelaifi said last year. “If we are going to make that happen, we have to win the Champions League. That will take the club to a new dimension. Any team that wins it is seen differently by everyone else.”

Still, progress had been made. Khelaifi was correct to assert that P.S.G. was now viewed by Europe’s biggest clubs as a “serious challenger” to win the competition. “Most of them want to avoid us in the last 16,” he said. “That is a mark of respect in itself.”

The problem is that progress has, in the last two years, stalled. The core of P.S.G.’s team — Silva, Thiago Motta, Edinson Cavani — arrived in Paris between 2011 and 2013, the first great flourish of the new Qatari owners’ largess.

The impact of more recent additions, apart perhaps from Ángel Di María, has been more limited; P.S.G. has proved unable to make the final leap from contenders to champions, finding, as so many do, that at the summit, the smallest steps are the steepest.