The path to conjoin London's

EMI Group

(EMI.L)

and Edgar Bronfman Jr.'s

Warner Music

(WMG)

is proving to be a long and winding one, with little visibility on a potential outcome.

Warner has now twice offered to buy EMI, while EMI has twice offered to buy Warner. Each has twice rejected the other.

On Wednesday, word emerged from EMI that Warner has made consecutive offers to buy the British recording giant, with the latest bid coming in at $4.56 billion. EMI, which has its own offer on the table for Warner, turned down the proposals.

EMI previously floated an offer to acquire the Bronfman-led Warner Music for $28.50 per share, or $4.2 billion. That offer was swiftly rejected by Warner's board. In a statement Wednesday, EMI said it raised the proposal to $31 a share -- and Warner rejected it again.

What is unclear is why the private equity interests in Warner Music, namely Bain Capital, Tom Lee Partners and Providence, wouldn't be happy to get out at the tidy premium implied by EMI's latest offer. Warner, however, has enjoyed several strong quarters and backers may feel that Bronfman has performed above expectations and can lead them to further glory in the industry.

That logic wouldn't necessarily prevent Warner's private backers from supporting a scenario in which Bronfman takes over EMI. The owners may believe in the synergies a larger music entity would create or feel they can exit through the public markets down the line.

Both EMI's offers for Warner and Warner's for EMI have been for cash. Sources says that the EMI offers have come with significant strings attached, including a condition that Warner sell its entire publishing business prior to a merger.

Warner Music shares got a lift Wednesday on word of the activity. At midday, they were trading up $1.28, or nearly 5%, to $28.51. In London, EMI shares rocketed over 8%, or 24 British pence, on bid talk.

In a statement, EMI said it "continues to believe that an acquisition of Warner Music by EMI at $31 per share in cash would be very attractive to both sets of shareholders and would deliver value to EMI's shareholders which is far superior to Warner Music's revised alternative proposal. The Board of EMI is committed to pursuing such a transaction only if it delivers enhanced value and earnings accretion to EMI shareholders."

Warner Music confirmed both the proposal and its rejection. "The WMG board had unanimously rejected EMI's revised proposal to acquire WMG at $31 per share in cash," it said, adding, "WMG board agrees with EMI that there are potential merits in combining the businesses of WMG and EMI, but believes that a WMG acquisition of EMI will provide shareholders of both companies with a superior opportunity to realize significant value."

The EMI proposal, says Warner, "also includes several important pre-conditions which increase execution risk. These include, in particular, the pre-sale of Warner/Chappell Music and underwriting a substantial rights offering."

If the two sides decide to merge they will surely face regulatory scrutiny in both the U.S. and in Europe. A joint group would create the world's third largest music company after Sony/BMG and Universal.