  The modified long-wavelength approximation (MLWA), a next order approximation
beyond the Rayleigh limit, has been applied usually only to the dipole $\ell=1$
contribution and for the range of size parameters $x$ not exceeding $x\lesssim
1$ to estimate far- and near-field electromagnetic properties of plasmonic
nanoparticles. Provided that the MLWA functional form for the $T$-matrix in a
given channel $\ell$ is limited to the ratio $T\sim iR/(F+D-iR)$, where $F$ is
the familiar size-independent Fr\"ohlich term and $R\sim {\cal O}(x^{2\ell+1})$
is a radiative reaction term, there is a one-parameter freedom in selecting the
dynamic depolarization term $D\sim {\cal O}(x^2)$ which preserves the
fundamental feature of the MLWA that its predictions coincide with those of the
Mie theory up to the order ${\cal O}(x^2)$. By exploiting this untapped design
freedom, we demonstrate on a number of different metals (Ag, Al, Au, Mg), and
using real material data, that the MLWA may surprisingly yield very accurate
results for plasmonic spheres both for (i) $x$ up to $\gtrsim 1$ and beyond,
and (ii) higher order multipoles ($\ell>1$), essentially doubling its expected
range of validity. Because the MLWA obviates the need of using spherical Bessel
and Hankel functions and allows for an intuitive description of (nano)particle
properties in terms of a driven damped harmonic oscillator parameters, a
significantly improved analysis and understanding of nanoparticle scattering
and near-field properties can be achieved.
