  In this paper, we explore the impact of extra radiation on predictions of $pp
\to t\bar{t}X, X = h/W^{\pm}/Z$ processes within the dimension-6 SMEFT
framework. While full next-to-leading order calculations are of course
preferred, they are not always practical, and so it is useful to be able to
capture the impacts of extra radiation using leading-order matrix elements
matched to the parton shower. While a matched leading-order calculation for
$t\bar{t}X$ is not expected to reproduce the next-to-leading order inclusive
cross section precisely, we show that it does capture the relative impact of
the EFT effects by considering the ratio of matched SMEFT inclusive cross
sections to Standard Model values, $\sigma_{\rm SMEFT}(t\bar{t}Xj)/\sigma_{\rm
SM}(t\bar{t}Xj) \equiv \mu$. Furthermore, we compare leading order calculations
with and without extra radiation and find several cases, such as the effect of
the operator $(\varphi^{\dagger}i\!\overleftrightarrow{D}_{\!\mu}\varphi)
(\bar{t}\gamma^\mu t)$ on $t\bar{t}h$ and $t\bar{t}W$, for which the relative
cross section prediction increases by more than $10\%$ -- significantly larger
than the uncertainty derived by varying the input scales in the calculation,
including the additional scales required for matching. Being leading order at
heart, matching has the benefit that it can be applied to all operators and
processes relevant to $pp \to t\bar{t}X, X = h/W^{\pm}/Z +$ jet, is
computationally fast and not susceptible to negative weights. Therefore, it is
a useful approach in $t\bar{t}X+$ jet studies where complete next-to-leading
order results are currently unavailable or unwieldy.
