  We consider Klein-Gordon (KG) particles in a global monopole (GM) spacetime
within Eddington-inspired Born-Infeld gravity (EiBI-gravity) and in a Wu-Yang
magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime
settings. We propose a textbook power series expansion for the KG radial wave
function that allows us to retrieve the exact energy levels for KG-oscillators
in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some
\textit{conditionally exact}, closed form, energy levels (through some
parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within
EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM
within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar
potential. We study and discuss the effects of the Eddington parameter
$\kappa$, GM-parameter $\alpha$, WYMM strength $\sigma$, KG-oscillators'
frequency $\Omega$, and the coupling parameters of the Coulomb plus linear
Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators
at hand. Such effects are studied over a vast range of the radial quantum
number $n_r\geq 0$ and include energy levels clustering at $\kappa>>1$ (i.e.,
extreme EiBI-gravity), and at $|\sigma|>>1$ (i.e., extreme WYMM strength).
