Capella Education Company acquired Resource Development International, which describes itself as the world's largest independent provider of UK university qualifications by distance learning, in a £9.3 million deal announced last month.
RDI had already applied for taught degree-awarding powers and, under the terms of the agreement, Capella will pay the £4 million premium if they are granted by July 2016.
Capella said the powers would enable RDI to "independently validate its own degrees going forward under the auspices of the Quality Assurance Agency", which it refers to in its press release as a "government body", despite the fact that the QAA is independent.
Critics say the deal again highlights the issues that were raised when BPP was bought by a subsidiary of the US giant Apollo Group after the UK provider had gained degree-awarding powers.
Roger Brown, professor of higher education policy at Liverpool Hope University, said that, in the case of RDI, it should be the new owner that applies for degree-awarding powers and the process should go back to square one. "The key question with degree-awarding powers is, who ultimately owns the powers?
"It doesn't matter if it is an American company or whatever - the question is who takes the ultimate decisions about the use of those powers," he said.
Sally Hunt, general secretary of the University and College Union, said the deal "once again highlights the danger of for-profit higher education and the lack of proper regulation in the government's White Paper".
She added that the application for degree-awarding powers "must immediately be reviewed".
Others suggested that ministers needed to provide clarity on the rules governing taught degree-awarding powers and how they applied to acquired companies.
Geoffrey Alderman, professor of politics and contemporary history at the University of Buckingham, said he was "surprised" that the recent consultation on the regulatory environment had been silent on the issue.
Carl Lygo, chief executive of BPP, said that while he believed the Apollo deal had voluntarily provided "safeguards" over the control of the powers, it would not be unreasonable for the government to set out rules for the future.
RDI, which had revenues of £8.6 million in 2010, currently offers distance-learning degrees validated by institutions including the universities of Wales, Sunderland and Birmingham, and Anglia Ruskin and Sheffield Hallam universities.
UK students form only about a quarter of its enrolments, but Kevin Gilligan, Capella's chief executive, has said that RDI has an opportunity to be "disruptive" and serve the UK "more aggressively".
Although not one of the largest US for-profits, Capella, which has 38,000 students enrolled in its own online Capella University, has been caught up in the controversy surrounding the industry there.
Official figures released last year showed that only 40 per cent of federal loans borrowed by Capella students were repaid.