  Neutrino oscillation in the matter could get affected by the sub-dominant,
yet unknown, non-standard interactions. The upcoming long-baseline (LBL)
neutrino experiments will be sensitive to these effects and can provide
information on the unknown oscillation parameter values. In this article, we
study the parameter degeneracies that can occur in DUNE, T2HK experiments, and
a combination of both due to nonstandard interactions (NSI), arising
simultaneously, from two different off-diagonal sectors, i.e., $e-\mu$ and
$e-\tau$. We derive constraints on both the NSI sectors using the combined
datasets of NO$\nu$A and T2K. Our analysis reveals a significant impact that
dual NSIs may have on the sensitivity of atmospheric mixing angle $\theta_{23}$
in the normal ordering (NO) case. Furthermore, when non-standard interaction
from the $e-\mu$ and $e-\tau$ sectors are included, we see significant changes
in the probabilities for DUNE, T2HK, and as well as a combined analysis
involving both. Moreover, the CP sensitivity gets affected significantly due to
the presence of dual NSIs, and, in addition, the CP asymmetry also exhibits an
appreciable difference.
