Atalanta announced a quadruple deal to bring in Ibrahim Sulemana from Cagliari, while sending Nadir Zortea, Michel Ndary Adopo and Roberto Piccoli to Sardinia.
The complicated agreement allows four players to move around with differing formulas and payment structures.
La Dea have purchased midfielder Sulemana from Cagliari for €8m.
At the same time, they sold full-back Zortea to the Sardinians for circa €5m.
The 25-year-old was a product of their youth academy and went on several loan spells, making 17 Serie A appearances with two goals for Atalanta.
Atalanta buy one, sell one, loan two
As for the other two, centre-forward Piccoli joins Cagliari on loan for €2m with an option to buy at the end of the season for a further €10m.
Midfielder Adopo, previously of Torino who joined Atalanta as a free agent last year, goes to the island on a free one-year loan with an option to make the move permanent, but in this case the figures are still somewhat sketchy.