In this work, we present fully π-conjugated diradical(oid)s and tetraradical(oid)s with five-membered non-alternant cyclopentadienyl and quasi-alternant thiophene rings, latter of which is used as a source of aromatic stabilization. By controlling the topology of the π-systems, we can restrict the lower-bound number of unpaired electrons. Aromaticity and/or anti-aromaticity in the different configurations of the compounds can be used to design conjugated compounds with high open-shell characters. We also designed the diradical(oid) based only on the five-membered rings, without any terminal radical groups. This work exemplifies the application of our theory of rational design of polyradicals with the heteroatomic and non/quasi-alternant organic systems. The ability to create polyradicals with different classes of organic compounds offers possibilities to create multifunctional organic materials with tunable magnetic properties.