We could build an industrious, Atlético type team without overspending to an extreme, and adding no more than 3-4 players:
-----------------------Martial
--------↗------------------------Griezmann
-----Pogba--------------------------------------------↖↑
-------------------Herrera----------Keïta-----------Mkhitaryan
Kolašinac-------------------------------------------------------Valencia
---------------------Giménez--------------Bailly
--------------------------------De Gea
Mandžukić and Torres alternated for them, and Martial is quite similar to the latter when he was at his peak. Will only happen if José is more flexible in his approach, though.
Mkhitaryan - Arda.
Pogba isn't entirely out of his comfort zone.
Ander is a bit like Gabi.
Keïta for Tiago - who could press and pass and dribble - in general, a good fit with Gabi.
Kolašinac only because he's a Mourinho type fullback in the Ivanović mold, is more refined than Shaw, provides better end product, and is available on a Bosman:
Depending on Shaw's improvement, he could easily make the spot his own, making Kolašinac a really good depth option as a leftback/central defensive option.
Giménez = Godín Jr.
Best part about it all - 2 of the most high profile additions have a buyout clause that can be activated if an agreement is reached with the player:
Giménez Griezmann, so there might not be protracted negotiations with the selling clubs dragging its heels unnecessarily.
Keïta has been a revelation at Leipzig (like Kanté at Leicester), possesses a great engine to pair with Herrera and will not be super expensive, apart from being technically decent and only 22 years old - so he could be a long term addition (like Giménez and Griezmann).
With the right amount of planning, we could finish all the summer business by May/June and have a productive summer tour/training program - which should hold us in good stead come next season. Instead of dragging things till August - which is quite disruptive.