The recent advances in photonic technology will allow deploying flexgrid-based optical core networks in the near future. Although that technology favors more efficient spectrum utilization, multilayer IP/MPLS-over-flexgrid networks would still be needed to groom together client flows, coming from access and metro networks, into optical connections. In this scenario, multi-flow transponders (MF-TPs) will provide additional flexibility allowing reconfiguration of optical connections to be performed. To be operated, a distributed control plane together with a centralized Path Computation Element (PCE) could be used. In the event of a failure, tens or hundreds of client flows could become disconnected and thus, restoration routes need to be found by the PCE for these flows. In standard restoration, path computation for each client flow is performed which derives into resource contention as a result of several connections trying to use some common resources, and poor resource utilization as a result of the reduction of grooming levels. In this paper, we deal with these problems and solve the DYNamic restorAtion in Multi-layer IP/MPLS-over-flexgrid Optical networks (DYNAMO) problem. Client flows' restoration requests are grouped into a single bulk in the PCE. Afterwards, a Global Concurrent Optimization (GCO) module solves the DYNAMO problem finding routes for all the flows in the bulk. The DYNAMO problem is modeled by using mathematical programming. However, as a consequence of its complexity and the stringent times within which the problem has to be solved, a GRASP-based heuristic is used. Exhaustive simulation results performed on two national core topologies show that a PCE with a GCO module solving DYNAMO highly improves restorability and reduces remarkably the number and capacity of MF-TPs, at the expense of some increment in restoration times.