Federated learning (FL) is the most popular distributed machine learning technique. However, implementation of FL over modern wireless networks faces key challenges caused by (i) dynamics of the network conditions, (ii) coexistence of multiple FL services/tasks in the system, and (iii) concurrent execution of FL services with other network services, which are not jointly considered in prior works. Motivated by these challenges, we introduce a generic FL paradigm over next-generation (NextG) networks, called dynamic multi-service FL (DMS-FL). We identify three unexplored design considerations in DMS-FL: (i) FL service operator accumulation, (ii) wireless resource fragmentation, and (iii) signal strength fluctuations. We take the first steps towards addressing these design considerations through proposing a novel distributed ML architecture called elastic virtualized FL (EV-FL). EV-FL unleashes the full potential of Open RAN (O-RAN) systems and introduces an elastic resource provisioning methodology to execute FL services. It further constitutes a multi-time-scale FL management system that introduces three dimensions into existing FL architectures: (i) virtualization, (ii) scalability, and (iii) elasticity. Through investigating EV-FL, we reveal a series of open research directions for future work. We finally simulate EV-FL to demonstrate its potential to save wireless resources and increase fairness among FL services.