Teenagers from the wealthiest families would be able to pay for extra places at the most competitive universities under government proposals that could allow institutions to charge some British students the same high fees as overseas undergraduates.

Candidates who take up the extra places would not be eligible for publicly funded loans to pay tuition fees or living costs, limiting this option to all but the most privileged households who could pay fees up front.

Under the plans, the extra students may be charged as much as international undergraduates. At the most competitive universities, these students face fees ranging from £12,000 a year for arts subjects to £18,000 for sciences and more than £28,000 for medicine. Applicants would be required to meet the course entry requirements.

The changes would give more students the chance to attend their first choice of university. At present, the government sets a quota of undergraduate places that English universities are allowed to offer each year.

Employers and charities will also be encouraged to sponsor "off-quota" places under the plans to be outlined in a higher education white paper in the summer.

Ministers argue that the creation of extra places will boost social mobility by freeing up more publicly subsidised places for undergraduates from poorer homes.

But the proposals are likely to be criticised as a means for the wealthiest to "buy places" at a time when the government is to cut 10,000 publicly funded places.

The universities minister, David Willetts, told the Guardian: "There are various important issues that need to be addressed around off-quota places, but I start from the view that an increase in the total number of higher education places could aid social mobility.

"There would need to be arrangements to make sure any such system was fair and worked in the interests of students as well as institutions. But it is not clear what the benefit is of the current rules, which, for example, limit the ability of charities or social enterprises to sponsor students.

"We are inviting ideas on the whole concept and we will listen very carefully to all the responses we receive."

The proposal is most likely to be taken up by highly selective institutions, which turn away thousands of qualified candidates a year. Oxford accepted slightly more than 3,000 British and EU undergraduates out of about 17,000 who applied for the current academic year.

That demand is due to intensify as the latest application figures show the number of candidates for this autumn has risen by 2.1% to about 633,000 – another record high.

The places may not be covered by access agreements, under which universities are required to outline how they will improve their proportion of students from state schools and deprived backgrounds.

Under one version of the scheme, universities might operate a "needs-blind" admissions process, which assesses all candidates regardless of their ability to pay, but then offers places off-quota to candidates from the most privileged homes.

The expansion of places will put greater pressure on less popular universities. Ministers have warned that undersubscribed institutions could have government-funded places withdrawn.

In a speech last month, the business secretary, Vince Cable, said: "Institutions could very well find themselves in trouble if students can't see value. In circumstances where places are unfilled, we might withdraw those places, and institutions should not assume they will easily get them back."

This is more likely to happen if more sought-after universities are free to expand in response to student demand.

The government is also keen to encourage more corporate sponsorship of university places. The accountancy firm KPMG has unveiled a plan to pay fees for students at universities including Durham, in a training programme leading to an honours degree in accounting.

These students also fall outside government restrictions on numbers, chiefly because they are on bespoke courses reserved for one firm's employees. They do not need financial support as KPMG covers their fees and pays them a salary.

The current version of the scheme is, in effect, an outsourcing of corporate training, but the range of education on offer could become more diverse in future.

Asked if KPMG planned to extend the scheme to other degree subjects, Simon Haydn-Jones, an associate partner at the firm, said: "Yes we do, in due course – most likely by enabling students to take a range of subsidiary subjects such as geography in combination with an accountancy-related degree.

"It is early days for our scheme, though, and we need to get it up and running first before we take any specific decisions on this."

The KPMG scheme begins at Durham and Exeter this autumn, and will be extended to Birmingham University next year. The firm ultimately expects to offer more than 400 places.

A third option for expanding university places without cost to the public purse is by encouraging charities to sponsor students. At present, if a charity wished to fund a group of students from poor backgrounds, those places would have to come out of a university's existing quota because of the risk that the students involved might need public support in future.

The forthcoming white paper is expected to encourage charity sponsorship, possibly by enabling students to renounce entitlement to public support.