The phrase "accepted with the understanding" is correct and usable in written English.
It can be used when indicating that something is agreed upon with a specific condition or awareness of certain terms.
Example: "The contract was accepted with the understanding that all parties would fulfill their obligations by the deadline."
Alternatives: "agreed upon with the condition" or "accepted with the awareness".
"Given my practical and applied experience in the stable isotope world, I decided to apply to work with Thermo, and was accepted with the [understanding] that the job wouldn't require me to move, but did require a heavy travel schedule".
A multidisciplinary approach to care is widely accepted with the increased understanding of the interplay between the biological, psychosocial, and sociological factors in SCD.
"The few who are invited to fully participate are accepted with an understanding that they cannot criticise German Christian culture and that if they succeed they are German and if they fail they are Turkish or Muslim".
Justice Fisher agreed with prosecutors, however, that the actions Justice Garson is accused of met the legal definition of criminal bribe-receiving: accepting gifts with the understanding that the gifts would influence his actions as a public servant.
It was an accepted part of the understanding — from the start.
She accepted, she said, with the understanding that it would lead to full-time work.
According to Mr. Frassinelli, the university accepted the gift with the understanding that it would very likely be sold off.
Mr. Lemke said he had accepted the money with the understanding that he could give the party money for operations and was not bound by any agreement not to distribute the funds.
I accepted the job with the understanding that I had an obligation to disagree with the unusual jurist.
This is what provides the common ground to make fruitful dialogue possible: we need to accept what we share in order to accept with civility and understanding what we most certainly do not.
