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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 SMEFTframework. While full next-to-leading order calculations are of coursepreferred, they are not always practical, and so it is useful to be able tocapture the impacts of extra radiation using leading-order matrix elementsmatched 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 inclusivecross section precisely, we show that it does capture the relative impact ofthe EFT effects by considering the ratio of matched SMEFT inclusive crosssections to Standard Model values, $\sigma_{\rm SMEFT}(t\bar{t}Xj)/\sigma_{\rmSM}(t\bar{t}Xj) \equiv \mu$. Furthermore, we compare leading order calculationswith and without extra radiation and find several cases, such as the effect ofthe 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 relativecross section prediction increases by more than $10\%$ -- significantly largerthan the uncertainty derived by varying the input scales in the calculation,including the additional scales required for matching. Being leading order atheart, matching has the benefit that it can be applied to all operators andprocesses relevant to $pp \to t\bar{t}X, X = h/W^{\pm}/Z +$ jet, iscomputationally fast and not susceptible to negative weights. Therefore, it isa useful approach in $t\bar{t}X+$ jet studies where complete next-to-leadingorder results are currently unavailable or unwieldy.

Matching in $pp \to t \bar{t} W/Z/h +$ jet SMEFT studies