Not in Find Mode, but there are ways for the user to enter such a list of information while in Browse mode and then a script can enter find mode and loop through such a list of criteria in order to generate the needed find requests, followed by performing the find.
You may find the script examples here helpful, though I don't recall one that is exactly like the scenario you describe: Scripted Find Examples
So I suggest reading it over first and then, if you still have questions, use Post a New Answer to reply back here and I'll build on the info in that thread to provide an example that might work for you.
Important Note: When you specify search criteria in fields from a related table--such as those found in a portal, you are still searching the layout's table for records, not the portal's. If you perform a find with such criteria specified, you are telling filemaker to: "Find all records in the layout table that match to at least one related record that has this specified criteria". Once the find is performed and the window returns to browse mode, each record thus found will display all related records in the portal--whether or not that portal record matches the search criteria that you specified.