In all cases of ablativus absolutus that I know, there is a main word and an attribute and both are in ablative. For example, me absente is "while I am away" and Caesare duce is "when Caesar is in charge". Is it possible to replace the attribute with a prepositional phrase or something else that does not contain an bare ablative (without preposition). I sometimes find myself tempted to use expressions like this:
Caesare Romae id fecimus. — We did it while Caesar was in Rome.
Pane in mensa edere coepimus. — We started to eat when the bread was in the table.
Ambulamus manu in manu. — We are walking hand in hand.
(There is also a separate question about the last one.) I suspect these are wrong and I have resisted the temptation hitherto, but I would like confirmation. Does the absolute ablative always require two parts, both of them in ablative? Are there examples like the ones I suggested? I know I can fix most such sentences by adding a participle (e.g. Caesare Romae versante or pane in mensa posito), but my question is whether such a participle is necessary.