Not by the standard user interface.
You have to write macros for this.
If you enter a simple selection, it is more or less possible by a macro. The selection then is done by that macro (by an inputbox).
It is all years a wish of me that search history in the client will be improved on a way that it could be translated to a search macro.
Search history is now not detailed enough for this.
That would be best solution for the wish you have (and I!). Search in db a, perform same search in db b - no matter how or what you did select in A.
I'm sorry to tell this function never (could?) be realised by Cardbox UK.
Although I can think of circumstances in which searching multiple databases could be useful, I wonder why it would be necessary to do so. A search typically consists of the term to search for and a field to search in. Searching through multiple databases would require fields to have the same name and to have similar content. Then why are they seperate databases? You may consider merging such databases into a single database.
Consider two databases, A and B, with let's say 7 fields. Five fields in A and B contain more or less similar data. Two fields are completely different. You could have a single database of 9 fields: the 5 comparable fields, 2 fields that were specific to A and 2 fields that were specific to B.
If it is necessary to distinguish between A and B you could simply add another field that contains either "A" or "B".
You could then search through all data in a single search and still have two sets of data.