Two Christian guesthouse owners are considering taking their legal fight against rulings of discrimination to the Supreme Court.
Judges have twice ruled Peter and Hazelmary Bull, from Cornwall, broke equality laws in 2008.
The couple had refused to allow civil partners Steven Preddy and Martyn Hall, from Bristol, a double room at Chymorvah House in Marazion.
The Christian Institute said it was backing Mr and Mrs Bull's case.
Mrs Bull said: "I feel that the law has gone too far. Certainly Pete and I are ready to see if we can achieve some sort of result whereby two lifestyles can live alongside each other.
"We need to apply for leave to appeal, because that wasn't given at the last court hearing. If we get it we could take it to the Supreme Court. If we don't get leave to appeal then I understand we would possibly take it to Brussels."
Mike Judge, from the Christian Institute, said: "I think this is a leading case, and it may even go to the European Court of Human Rights if we are not successful at the Supreme Court."
Mr Judge said Mr and Mrs Bull had applied their policy to all unmarried couples, not just same-sex couples.
Dr Michael Halls, from the South West-based charity the Intercom Trust, which works with lesbian, gay, bisexual and transgender communities, said: "[Mr and Mrs Bull] were discriminating against marriage and civil partnership.
"I think the conflict of rights in this case will be decided against them," he added.
In February, Mr and Mrs Bull took their case to the Court of Appeal and lost their appeal against a ruling that they had acted unlawfully.
They had appealed against a conclusion by a judge at Bristol County Court that they acted unlawfully when they turned the couple away.