This work aims to evaluate the spinnability of recycled poly(ethylene terephthalate) (rPET) modified by chain extenders. Pyromellitic anhydride (PMDA), JONCRYL ADR 4400, 2,2′-bis(2-oxazoline) (BOZ), and 1,3-phenylene-bis-oxazoline (PBO) were used from 0.1 to 1 wt% on transparent postconsumer PET bottle flakes and opaque rPET flakes containing TiO2 particles. The created molecular architectures were characterized in the first section. Second, their spinnability was assessed via a pilot high-speed spinning process. The corresponding shear rheology, intrinsic viscosity, and elongational rheology were reported. It was observed that PMDA and JONCRYL induce a more drastic increase in melt strength and melt elasticity than BOZ and PBO due to chain branching. In a second step, melt-spun filaments were produced with a low content of chain extenders on standard rPET and opaque rPET matrices. Finally, their degree of crystallinity, molecular orientation, and mechanical properties were determined. PMDA and JONCRYL strongly decrease the spinnability and, consequently, the properties of filaments. However, BOZ improves the opaque rPET filaments’ tenacity while decreasing their degree of crystallinity.