We report the failure of coupled-cluster valence-bond (CCVB) theory with twopair configurations [J. Chem. Phys. 2009, 130, 084103 (2009] for open-shell (OS) spin-frustrated systems where including three-pair configurations is necessary to properly describe strong spin-correlations. We extend OS-CCVB by augmenting the model with three-pair configurations within the independent amplitude approximation (IAA).The resulting new electronic structure model, OS-CCVB+i3, involves only a quadratic number of independent wavefunction parameters. It includes the recently reported closed-shell CCVB+i3 as a special case. Its cost is dominated by integral transformations and it is capable of breaking multiple bonds exactly for all systems examined so far. The strength of OS-CCVB+i3 is highlighted in realistic systems including the [CaMn 3 O 4 ] cubane subunit of the oxygen-evolving complex and a molecular magnet with the [Cr 9 ] core unit as well as model systems such as N 3 , V 3 O 3 , and P 5 . We show that OS-CCVB+i3 is only slightly dependent on the underlying perfect-pairing reference while OS-CCVB shows a stronger dependence. We also emphasize the compactness of the OS-CCVB+i3 wavefunction compared to the heat-bath configuration interaction wavefunction, a recently introduced soft exponential-scaling approach.