Earlier quoted context omitted.
In English, maybe; in Russian, I frequently find myself reaching for the nonexistent “morphology but not synonyms” operator (as the same noun phrase can take a different form depending on whether it is the subject or the object of a verb, or even on which verb it is the object of); even German should have the same problem AFAIU, if a bit milder. I don’t dare think about how speakers of agglunative languages (Finnish,…
Ah, OK. I don’t know anything about Russian. This is a hard problem. I think the solution is something like what you suggest: more operators allowing different transformations. Even in English, I would like a "you may pluralize but nothing else" operator.
There are six of them (nominal [subject], genitive [belonging, part, absence, “of”], dative [indirect object, recipient, “to”], accusative [direct object], instrumental [device, means, “by”], prepositional [what the hell even is this]), so you have (cases) × (numbers) = 6 × 2 = 12 noun forms, and adjectives agree in number and gender with their noun, but (unlike Romance languages) plurals don’t have gender, so you have (cases) × (numbers and genders) = 6 × (3 + 1) = 24 adjective forms.
None of this would be particularly problematic, except these forms work like French or Spanish verbs: they are synthetic (case, number and gender are all a single fused ending, not orthogonal ones) and highly convoluted with a lot of irregularities. And nouns and adjectives are usually more important for a web search than verbs.