  A Steiner triple system, STS$(v)$, is a family of $3$-subsets (blocks) of a
set of $v$ elements such that any two elements occur together in precisely one
block. A collection of triples consisting of two copies of each block of an STS
is called a duplicated Steiner triple system, DSTS. A resolvable (or near
resolvable) DSTS is called self-orthogonal if every pair of distinct classes in
the resolution has at most one block in common. We provide several methods to
construct self-orthogonal near resolvable DSTS and settle the existence of such
designs for all values of $v$ with only four possible exceptions. This
addresses a recent question of Bryant, Davies and Neubecker.
