They are also planning to introduce some lower-priced tickets when the building reopens at the end of 1999 after its pounds 213m redevelopment.
They are considering introducing matinees and performances set at different price levels - high-priced ones exclusively for corporate and subscriber opera goers and ones open to the public with more middle- and lower-priced seats.
Chris Smith the Secretary of state for Heritage, warned the Royal Opera House that it might lose its annual pounds 14.5m grant unless it cut its prices and improved its "elitist" image.
Mark Fisher, the Arts Minister, said a new approach was essential. The Royal Opera must become the people's opera house, serving the whole nation, he said.
The Sunday-opening scheme was revealed by Keith Cooper, Covent Garden's director of public affairs. He said 100 extra lower-priced seats were being created in the amphitheatre as part of the reshaping. There would be 20 per cent more performances.
There was "no problem" in finding corporate clients willing to pay pounds 125 to hear international stars such as Placido Domingo, he added.
"But we have to find more mid- and low-priced seats more regularly and more widely available."
He foresaw different price levels for corporate clients, subscribers and the public.
The Royal Opera runs up to its closure in July with two new productions of Verdi operas. The crisis-dogged production of Macbeth is being sung in a concert version because of lack of time for technical rehearsals but the new Simone Boccanegra, premiered on Saturday, is lushly costumed and with dramatic scenery.
The international cast is headed by Placido Domingo as Gabriele Adorno and the distinguished Russian baritone Sergei Leiferkus in the title role. It will be broadcast live on BBC Radio 3 on Friday evening.
The final performance before the Royal Opera's closure will be on 14 July when the Prince of Wales and Princess Margaret, respectively patron of the Royal Opera and President of the Royal Ballet, attend a farewell gala.
During the closure the companies will perform at a variety of venues in London, including Barbican and the Albert Hall.