The phrase "most deeply involved" is correct and usable in written English.
It can be used when describing someone or something that is heavily or deeply involved in a situation or activity. Example: The team's star player was most deeply involved in the championship game, scoring three goals and leading the team to victory.
Beyond his leadership responsibilities, Mr. Cheney was most deeply involved in foreign policy and intelligence matters.
This was when Varella was most deeply involved in his Carandiru project.
The league said they were the most deeply involved in the bounties while they were with the Saints.
Ironically, one of the most conspicuous laggards in providing these police officers is France, the country whose troops have been most deeply involved in the Mitrovica strife.
The five senators most deeply involved in writing the election bill said tonight that they would continue talks in hopes of achieving agreement.
Of all the photographers who have been walking the art-fashion tightrope of late, Philip-Lorca diCorcia is probably the most deeply involved.
"Proof" is one of the most deeply involving dramas available in modern theater catalogues, and its record of dynamic productions is strongly continued at WCT.
For recovery to succeed, the most vulnerable must be deeply involved in the creation and implementation of the national housing plan.
Most important, he was deeply involved with the French Board of Longitude, even serving as president, sending teams of soldiers and surveyors across the oceans to map the far-flung empire.
Hermeneutics (the art and discipline of interpretation), of which Gadamer is one of the twentieth century's most formidable exponents, is deeply involved in philosophical disputes over the legitimacy of claims to understanding in the visual and literary arts.
The global nature of their competition meant that both superpowers became deeply involved in most world trouble spots.
