  Multimode cavity quantum electrodynamics ---where a two-level system
interacts simultaneously with many cavity modes---provides a versatile
framework for quantum information processing and quantum optics. Due to the
combination of long coherence times and large interaction strengths, one of the
leading experimental platforms for cavity QED involves coupling a
superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D
multimode circuit QED system with single photon lifetimes of $2$ ms and
cooperativities of $0.5-1.5\times10^9$ across 9 modes of a novel seamless
cavity. We demonstrate a variety of protocols for universal single-mode quantum
control applicable across all cavity modes, using only a single drive line. We
achieve this by developing a straightforward flute method for creating
monolithic superconducting microwave cavities that reduces loss while
simultaneously allowing control of the mode spectrum and mode-qubit
interaction. We highlight the flexibility and ease of implementation of this
technique by using it to fabricate a variety of 3D cavity geometries, providing
a template for engineering multimode quantum systems with exceptionally low
dissipation. This work is an important step towards realizing hardware
efficient random access quantum memories and processors, and for exploring
quantum many-body physics with photons.
