Speaking as a native speaker of British English, "We can agree another date" is perfectly acceptable. "On" is optional, albeit the most common variant. Here's the Google Ngram: https://books.google.com/ngrams/graph?content=agree+a+date%2Cagree+on+a+date%2Cagree+to+a+date&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cagree%20a%20date%3B%2Cc0%3B.t1%3B%2Cagree%20on%20a%20date%3B%2Cc0%3B.t1%3B%2Cagree%20to%20a%20date%3B%2Cc0
I'm wondering if the meaning is not that we can agree on the date, but that we can make the decision another day. We want to decide something, we can't agree, so let's meet another day (date) to decide. I feel like if it was "we can agree on another date", we'd need a preposition before "un'altra data". "Possiamo concordare su un'altra data" = "We can agree on another date." Any native speakers out there?
I am a native speaker of English. Whether or not the meaning of the Italian phrase is that "we can agree on another (an alternative) date" or "another day (but not today) we can agree", no native speaker of English would say "we can agree another date." I'll report it and see if they revise it.
Me too, and I'm not alone: "the State concerned shall inform the other State before the expiry of the period and the two States shall agree another date for the extradition."
(from Algeria No. 3 (2006) Convention between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the People’s Democratic Republic of Algeria on Extradition)
It seems to be O.K. for our lawmakers.