Deriving a computationally-efficient counterpart of a CFD model, i.e., reduced-order modeling (ROM), has attracted much interest for various time-critical applications where a high-fidelity model simulation is desired at a minimal computational cost. Despite the surging interest in ROMs, there still exist major hindrances to their industry-wide adoption. Many existing techniques rely on access to the discretization operator of the CFD model, which is often unavailable for general-purpose CFD softwares suitable for practical applications. The performance of data-driven ROMs can also vary widely depending on how training data are selected. Note many of the data-driven ROM techniques originate from conventional system identification and data compression techniques for an actual system. With an actual system, while its excitation conditions can be manipulated to improve identification, its physical parameters such as input source location should remain intact. Our team has been implementing a new concept of altering the digital twin, i.e., CFD Model, of the target system for improved identification. In the proposed approach, the CFD model is altered and excited as prescribed by the Krylov subspace method so that a physics-based ROM (equipped with superior generalizability) can be built using response data only. This alter-and-excite (A&E) approach can potentially overcome the limitations of both conventional and data-driven approaches by obviating the need for the CFD model operator and judicious choice of training data.