The phrase "admittedly the most" is correct and usable in written English.
It can be used when acknowledging a fact or opinion that may be considered subjective or debatable, often to introduce a statement that may be seen as controversial or surprising.
Example: "Admittedly the most challenging aspect of the project was coordinating the team’s efforts across different time zones."
Alternatives: "undeniably the most" or "arguably the most".
Why is this group of eight people around a table, admittedly the most powerful countries in the world, but why are they setting the agenda?
Though he's already forayed into horror with his 2011 interactive short, Take This Lollipop; he's perhaps not admittedly the most sensitive filmmaker to take on what's a difficult, uncomfortable part of Japan's cultural geography.
Admittedly, the most dangerous transgressions taking place in Mallory Towers invariably involved the cracking open of a tin of sardines a few minutes after midnight, but the jolly hockey sticks life still appealed.
Admittedly, the most commonly used technique for valuation of derivatives hinges on the concept of replication.
Admittedly, the most important aspect of accepting rules is compliance with them.
Admittedly, the most Republican tax credit plans made the tax credit contingent on securing "adequate" health insurance coverage (where "adequate" was defined much less stringently than under Obamacare).
Business continuity management is, admittedly, not the most exciting phrase.
The lowest car insurance quotes, after airline captains, goes to china restorers and toy makers – admittedly not the most racy of professions.
In Richard Lapchick's long battle against racial bias in sports, numbers have been his oral weapon of choice, reliable and irrefutable, though admittedly not the most effective means of commanding a room.
Otto started playing for Haringey Borough and his performances were good enough for the Southend United manager Barry Fry – admittedly not the most risk-averse man in the world – to fork out £100,000 for him.
That is admittedly not the most upbeat night out – and poor Alfred spent the evening before swotting up by watching the film in its entirety, which is quite a lot of time spent with a rather grim subject – but he was impressed by the results, as you can read in his four-star review of the show here.
