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Polymer topology highly impacts rheological melt and foaming properties. Grafting sidechains onto a linear polymer typically results in shear thinning and strain hardening in elongation flow. To study the influence of an increasing number of covalently connected polystyrene (PS) stars s with a linear PS chain (Mw,PS = 90 kg mol−1), low‐disperse branched polymers with s ranging from one to four are synthesized. Each star contains approximately 12 sidechains with a length of Mw,a≈ 25 kg mol−1. Oscillatory shear measurements indicated that the zero‐shear viscosity η0 scales with η0 ≈ Mw,t3.9$M_{w,t}^{3.9}$ at Tref = 180 °C. Moreover, uniaxial elongation rheology allows determining the strain hardening factor SHF, which varies between SHF = 2–135, with increasing s. Foaming experiments revealed that combining viscosity reduction with the improvement of stretchability promotes higher volume expansion ratios (VER = 3.21–10.41) and the formation of larger cells (D = 4.8–14.8 µm). [ABSTRACT FROM AUTHOR]