Hi,
I don’t know if this is possible – because only typing the keyword “carrot” there is no way for the plugin to know you also mean “potato”.
Depending on how you want to restrict the results, you can try a restriction by post tags, but that will apply to all search phrases.
Another sort of a “hacky” way is to try keyword replacements programmatically via this tutorial. You could add rule so when “carrot” keyword is typed, it is replaced with “potato carrot”.
'carrot' => 'potato carrot',