The group of nations known as BRICS — Brazil, Russia, India, China and South Africa — represents 40 percent of the world’s population and a quarter of the world’s economy. Now it is considering expanding, in a push to be seen as a credible counterweight to Western-led forums like the G7 group of advanced nations.

But the challenge for the club is that it is as divergent as it is large, and hindered by sometimes conflicting interests and internal rivalries. It comprises the world’s largest authoritarian state (China) and its largest democracy (India), economies big and small, and relations with the United States that run the gamut, from friend to foe.

China, under Xi Jinping, wants to expand BRICS, seeing in it a platform to challenge American power. Russia is keen to demonstrate that Moscow has loyal allies despite its isolation from the West over the war in Ukraine. India, locked in a territorial dispute with China, is wary of Beijing’s dominance in the club.

Brazil and South Africa, the other swing states of the developing world, want good relations with China and Russia, but not to be overly aligned with either, for fear of alienating the United States.

As leaders of the five nations meet starting Tuesday at an annual summit, this time in Johannesburg, how they navigate those differences might determine whether the group becomes a geopolitical coalition or remains largely focused on financial issues such as reducing the dominance of the dollar in the global economy.

The task of finding common ground is only getting harder as the great power competition between Beijing and Washington intensifies, placing pressure on other nations to choose sides. And as Russia’s war in Ukraine grinds on, the conflict is roiling food and energy prices for many of the poorer countries that BRICS members claim to represent.

“China under Xi is looking to use BRICS for its own purposes, particularly in extending its influence in the Global South,” said Steve Tsang, the director of the SOAS China Institute in London. “India is highly unlikely to go along with it as the Chinese proposal will turn BRICS into something else — one which will serve primarily Chinese interests.”

Dozens of countries have expressed interest in joining the club. They include countries that fall squarely in the Chinese camp, like Iran and Belarus, and nonaligned states such as Egypt and Kazakhstan, reflecting a desire to hedge between China and United States in the face of geopolitical polarization.

The question of expansion will be leading the agenda of the three-day summit, to be attended in person by President Xi of China, Prime Minister Narendra Modi of India, President Luiz Inácio Lula da Silva of Brazil and President Cyril Ramaphosa of South Africa.

President Vladimir V. Putin of Russia is expected to take part remotely. Mr. Putin, who is wanted by an international court that has accused him of war crimes, had earlier planned on attending in person. He decided against it, sparing South Africa the dilemma of whether to arrest him.

China, which as the biggest economy in the group holds significant clout, will want to use the club to show that Beijing has its own circle of influence, after President Biden held a summit strengthening alliances last week with Japan and South Korea, nations in China’s backyard.

Beijing favors a rapid expansion of BRICS, which would also allow China to argue it has widespread support from the developing world.

“The Global South is not happy about the G7 trying to represent them, so they’re voting with their feet to join BRICS,” said Henry Huiyao Wang, president of the Center for China and Globalization in Beijing.

India has signaled that it prefers a more cautious approach that would limit Beijing’s ability to use the BRICS club to confront the West. It will want to avoid diluting its own role in favor of countries that might pick China over India in any tussle for influence.

India’s divergence with China reflects wider tensions and distrust between the two countries that were inflamed by a deadly border clash in 2020 and by India’s participation in a security grouping with the United States, Japan and Australia called the Quad.

India has emphasized that it is open to enlarging BRICS in principle, but wants to develop standards for deciding on new members, and to ensure that any changes are based on consensus.

Brazil has a similar position on the acceptance of new members.

“If they comply with the rules that we are establishing, we will accept their entry,” President Lula of Brazil told reporters this month.

Some of the requirements likely to be discussed include a minimum population or gross domestic product, as well as a willingness to work with the bloc’s New Development Bank, said one Brazilian government official helping plan for the talks who is not authorized to speak publicly and spoke on the condition of anonymity.

Brazil wants the group to remain a club of large, emerging economies rather than a geopolitical alliance that could be perceived as an anti-Western bloc, said a second Brazilian official helping to plan for the talks.

Mr. Lula said he supported at least three countries joining BRICS: Saudi Arabia, the United Arab Emirates and Argentina. He also suggested that Indonesia, which is widely seen as a natural fit given its size and location, would be a welcome addition.

An expansion, though, could make consensus in BRICS even more elusive. “When you have more countries join, and it’s such a disparate group to begin with, it’s harder to get anything accomplished,” said Theresa Fallon, director of the Center for Russia Europe Asia Studies in Brussels.

From Russia’s perspective, the summit will provide an opportunity to to court the developing world again, after Mr. Putin hosted African leaders in St. Petersburg this summer. .

But the foreign minister of Russia, Sergei V. Lavrov, who will travel to South Africa in Mr. Putin’s place, will likely face questions about why Russia pulled out of a United Nations-brokered deal with Ukraine that allowed the export of grain through the Black Sea. Food prices jumped after the collapse of the agreement.

BRICS members have struggled to show consensus on Russia’s war in Ukraine: China has leaned toward the Kremlin, while India has relied on a strategy of nonalignment. Brazil has offered rhetoric but little action.

South Africa, the group’s smallest member in terms of population and economy, has faced international and domestic criticism for its close ties to Moscow.

South Africa made a show of its neutrality when its president, Mr. Ramaphosa, led a peace mission of African leaders to meet with Mr. Putin and President Volodymyr Zelensky of Ukraine last month. Still, those talks are yet to yield tangible results.

South Africa bowed to Western pressure when it asked Mr. Putin to attend the summit virtually because of his arrest warrant. But the country is still trying to assert itself, defying what it sees as arm-twisting from the West to isolate Russia. Zaheer Laher, an official in South Africa’s foreign affairs ministry, went so far as to liken Russia’s isolation to “cancel culture.”

South Africa, the last country to join the bloc, in 2010 on China’s invitation, will also have to walk a fine diplomatic line with its allies in the West. In the coming months, South Africa will turn its attention to its second largest trading partner after China — the United States — hosting a meeting about a continental trade agreement.

“It almost feels that in South Africa, the heart is in the east, the money is in the west,” said Gustavo de Carvalho, a researcher at the South African Institute of International Affairs.

Olivia Wang contributed research.