1. have designs on - Verb
2. have designs on - Phrase
have designs on (third-person singular simple present has designs on, present participle having designs on, simple past and past participle had designs on)
(transitive) To have one's eye on, to set one's sights on, to seek, to pursue.
Both sides will have designs on getting promoted. Source: Internet
Third, it’s awfully late in the de Blasio administration for mayoral appointees to have designs on previously shared space.” Source: Internet