re: Construct a realistic playoff team under the following criteria.

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You can’t roll a sign and trade into a trade with multiple other players. To my knowledge.

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Yes you can.

The Knicks acquired Kyle O’Quinn in a 2015 sign-and-trade, while the Grizzlies and Bucks signed-and-traded for Troy Daniels and Matthew Dellavedova, respectively, in 2016. In 2017, the Clippers acquired Danilo Gallinari via sign-and-trade. No sign-and-trade deals were completed in 2018.