The design of globally \(C^s\)-smooth (\(s \geq 1\)) isogeometric spline spaces over multi-patch geometries is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods 25,28 and 31-33 for the construction of \(C^1\)-smooth and \(C^2\)-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of \(C^s\)-smooth isogeometric multi-patch spline spaces of an arbitrary selected smoothness \(s \geq 1\). More precisely, for any \(s \geq 1\), we study the space of \(C^s\)-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular \(C^s\)-smooth subspace of the entire \(C^s\)-smooth isogeometric multi-patch spline space. We further present the construction of a basis for this \(C^s\)-smooth subspace, which consists of simple and locally supported functions. Moreover, we use the \(C^s\)-smooth spline functions to perform \(L^2\) approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed \(C^s\)-smooth subspace.