Can we say "Did you fix me that account?" Or should it be "Did you fix that account for me?" assuming something is wrong with the account. Account represents a computer based system user id.
It is always
if it is your own account.
Ditransitive constructions in English do seem to occur idiosyncratically (I can't avoid that word!) rather than predictably. English Ditransitive Verbs: Aspects of Theory ... - by Joybrato Mukherjee (some parts available online) gives a good analytical overview of prototypical to peripheral examples. Colleman and De Clerk ( http://benjamins.com/series/fol/15-2/art/02col.pdf ) also give a good and thorough treatment, including a table of 'Ditransitive verb classes in English and associated constructional subsenses'. (A list!)
There does seem to be a gradual increase in the number of verbs, and number of allowable direct objects, used in such structures. 'Pick me a bunch of flowers' seems more common nowadays. The multi-word verb variant "fix me up a" gives a lot of returns, with diverse object types, in a Google search. The expression 'led her a merry dance', surely involving a reduced prepositional phrase, has acquired a similar form as a ditransitive construction, and 'led them a wild goose chase' is becoming more common.