Although neither can go ssj3 as vegeta never mastered it and the strain would be too much on the fusion possibly killing them it was stated the transformation could kill goku only reason he doesn't die is he was already dead when he used it
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But what about Gotenks? Trunks and Goten could only go super saiyan but still used it in the fusion. Plus they could substain it and they are kids
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Plus trunks and goten only could go ssj3 for a short time because it drained their energy which is how he lost to buu in the first place
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The potara earrings wouldn't allow the transformation because goku had to lower his power level so they were on a par with each other