  Non-orthogonal multiple access (NOMA) allows users sharing a resource-block
to efficiently reuse spectrum and improve cell sum rate $\mathcal{R}_{\rm tot}$
at the expense of increased interference. Orthogonal multiple access (OMA), on
the other hand, guarantees higher coverage. We introduce partial-NOMA in a
large two-user downlink network to provide both throughput and reliability. The
associated partial overlap controls interference while still offering spectrum
reuse. The nature of the partial overlap also allows us to employ
receive-filtering to further suppress interference. For signal decoding in our
partial-NOMA setup, we propose a new technique called flexible successive
interference cancellation (FSIC) decoding. We plot the rate region abstraction
and compare with OMA and NOMA. We formulate a problem to maximize
$\mathcal{R}_{\rm tot}$ constrained to a minimum throughput requirement for
each user and propose an algorithm to find a feasible resource allocation
efficiently. Our results show that partial-NOMA allows greater flexibility in
terms of performance. Partial-NOMA can also serve users that NOMA cannot. We
also show that with appropriate parameter selection and resource allocation,
partial-NOMA can outperform NOMA.
