My understanding of TPEs is they cannot use it as outgoing salary in a trade, you can only use it to absorb salary coming in. It's not a contract that can be traded, it's just a coupon that can be used to absorb incoming salary. So we could absorb a player up to $27m without sending out salary in return, but we can't say let's use the $27m Simons TPE and add another $27m in salary to get Giannis to make our Big 3.
What I think we could do is use the $27m TPE to absorb a player up to that value, then use that player in a package with other riffraff vet mins (maybe you S&T Vucevic for $12m which would hard cap Milwaukee) and Hauser for Giannis. Because then you have converted the TPE to actual salary that can be sent out. But I have to look at the rules as to the timing of when you can trade the player you got via the TPE.
The other roster building implications of such a move would be that you now have $170m of your $165m cap on 3 players, two of who have suffered serious injuries, and a third (Jaylen) who has not played more than 72 games a season since 2028-19. Then you have White (assuming you didn't trade him in the superteam building scenario) for $30m, which brings you to the luxury tax line with 4 players. Then you need to fill out the other 11 players on your roster, with the constraints being: to stay under the $209m first apron you can only spend up to $9m on all 11 (average of less than $1m a player); or to stay under the $222m 2nd apron you can only spend $22m on all 11 (average of $2m a player).
This scenario would remind me of the Suns with KD, Beal and Booker - and those 3 were only taking up $153m of their cap. Or the Sixers with Embiid, PG13 and Maxey. All you need is a chemistry fail or an injury and you're in a very tight spot, because once you're over the 2nd apron you can't aggregate salaries in trade, and can't use exceptions, and can't take in more salary than you send out.