Although I am not 100% sure, I think this sentence would have to use the subjunctive, so the sentence should read as follows
"The parties unanimously propose that the Office approve the registration..."
I believe "unanimously" can be used, especially if there are more than two parties which are united in the proposition.
The Subjunctive is used after the following verbs:
to insist to propose
The Subjunctive is used after the following expressions:
It is best (that) It is crucial (that) It is desirable (that) It is essential (that) It is imperative (that) It is important (that) It is recommended (that) It is urgent (that) It is vital (that) It is a good idea (that) It is a bad idea (that)