Paris St.-Germain has dominated domestic competition for nearly a decade, its team strengthened annually by the signings of expensive stars from around the world. But the title it covets most, the Champions League, remains elusive.

That description applies, of course, to the Paris St.-Germain men’s soccer team. But it also fits the club’s handball team, its sporting doppelgänger of sorts. Like the more prominent soccer team, the handball side never seems to lose in France. And like the soccer team, it just can’t seem to get over its final hurdle in European competition.

The men’s soccer team has won seven of the last nine French league titles and is almost certain to win this year as well. But its European record is spotty for a team of its enormous wealth: It has appeared in 10 straight Champions Leagues, but has only one runner-up finish, in 2020, and one other semifinal appearance to show for it.

The handball team wears the same blue uniforms and has — maddeningly, if you’re P.S.G. — trod the same path. It has won seven straight league titles, and this year there hardly seems to be any point in watching its domestic games: It is 21-0 and running away with another championship.

But its Champions League frustration will sound familiar: Over the last eight seasons, Paris St.-Germain has never failed to reach at least the quarterfinals, but it has only once advanced to the final. That year, 2017, it endured a crushing 24-23 loss to Vardar of Macedonia, a game decided on the last shot.

Qatar Sports Investments acquired Paris St.-Germain and its soccer team in 2011, and added the handball team — which had previously operated as part of a partnership with the club — to its fully owned portfolio in 2012. While they were solid first-division teams for much of their histories, neither the soccer team nor the handball team had been a worldbeater. But a flood of money from the new Qatari owners aimed to change that.

Paris St.-Germain has for years signed international soccer stars, including the two most expensive transfers in history: Neymar for $262 million in 2017 and Kylian Mbappé for $216 million in 2018. The biggest recent arrival was Lionel Messi, the Argentine midfielder who was a key part of the Barcelona team that humiliated P.S.G. in the Champions League in 2017.

The handball team — operating with a lower profile and a smaller budget — turned to the same playbook by acquiring two players acclaimed as among the greatest of all time: Mikkel Hansen, the Danish Olympic gold medalist, who has played with the team since 2012, and Nikola Karabatic, a three-time Olympic gold medalist for France, who was signed in 2015.

When Hansen was re-signed in 2017 for another five years, the P.S.G. executive Jean-Claude Blanc told Handball Planet: “The extension of Mikkel confirms the status of Paris St.-Germain handball on the world stage and our ambition for the coming seasons.” While title after title in France has been nice, though, that ambition also includes a European title or two.

Paris St.-Germain’s quest for a Champions League title this season sustained a blow when Hansen, a three-time world player of the year, contracted phlebitis and then a pulmonary embolism. He is out for the season and plans to return to a Danish club next season at age 34. Paris St.-Germain starts the playoff round against Elverum of Norway on Wednesday.

Should P.S.G. handball defeat Elverum and then Kiel of Germany, it would advance to a single-elimination final four in Cologne, Germany, in June, its sixth trip to that stage in seven years.

By then, plenty of opposing fans will again have accused Paris St.-Germain of paying for European glory. The payments have been made. But the glory remains — for now — just out of reach.