DUBAI, June 2 (Reuters) - Saudi Arabia added four more banks for its secondary share offering of oil giant Aramco , as the advisers began taking orders on Sunday for the sale that could eventually raise up to $13.1 billion, 4-1/2 years after its record initial public offering.

The Saudi government may sell up to a 0.7% stake in the world's top oil exporter. The banks on the deal will take orders through Thursday and it will price the following day, with the shares expected to start trading next Sunday on Riyadh's Saudi Exchange.

The investment banks added to the deal since it was announced on Thursday are Credit Suisse Saudi Arabia - part of UBS Group - as a domestic bookrunner alongside BNP Paribas, Bank of China International and China International Capital Corporation as foreign bookrunners, according to a stock exchange filing.

Already on the deal were Saudi National Bank's investment banking arm, which is the lead manager as well as global coordinator alongside Citi, Goldman Sachs, HSBC, JPMorgan, Bank of America and Morgan Stanley. Al Rajhi Capital, Riyad Capital and Saudi Fransi are also domestic joint bookrunners.

M. Klein and Company and Moelis are independent financial advisers for the deal.

The deal kicks off as the OPEC+ group of oil producers is set to meet on Sunday to determine output policy, with some ministers meeting in Riyadh, according to OPEC+ sources.

The de facto Saudi-led Organization of the Petroleum Exporting Countries and allies led by Russia, together known as OPEC+, is currently cutting output by a total of 5.86 million barrels per day (mbpd), equal to about 5.7% of global demand.

The curbs include a 1 mbpd voluntary cut by Saudia Arabia. While the moves by OPEC+ have helped support crude prices this year, Brent settled below $82 a barrel on Friday, down nearly $10 from a six-month high in April.

Aramco has boosted its dividends, introducing a new performance-linked payout mechanism last year, despite lower profits as a result of the lower volumes.

Saudi Arabia will first offer investors 0.64% of Aramco, or about 1.545 billion shares, at 26.7-29 riyals ($7.12-$7.73), translating to just under $12 billion at the top end of the range. A so-called greenshoe option could then be exercised for roughly 1.7 billion shares to be offered, or 0.7% of Aramco, to raise over $1 billion more.

Aramco exercised a greenshoe option after its IPO in late 2019, which remains the world's biggest.

About 10% of the new offering, excluding the greenshoe option, will be reserved for retail investors, subject to demand. ($1 = 3.7508 riyals) (Reporting by Yousef Saba; Editing by Emelia Sithole-Matarise)