Yes, FileLocator Pro supports subsequent searches within the text. FileLocator Pro has an extra tab called the Text Tab, which is basically a read-only text editor. The searched for text is highlighted and you can also search for additional phrases in the text, which will be highlighted in a different color:
The two highlighted options shown on the context menu allow you to either Search Again (ie re-run the whole search) for the highlighted word or Find (ie just search in the current text) a highlighted word. Alternately you can just type the text to search for in the Find edit box in the top row.
If you want to view the text in a larger window you can open the Text Tab as a separate top level tab by picking the Open in New Window... menu option.
More information is available in the online help: Internal File Viewer
Search within results
FileLocator Pro also has a search within results feature where you can select certain files from the result list and choose Search within selection to create a new search based on just those files.
Another 'drill-down' feature of FileLocator Pro is the ability to use the column filters feature to filter which files are displayed in the list: