He earned a subsequent loan move to Grosseto on 31 January 2011. He made his debut in Serie B on 5 February 2011, in Grosseto's 1–0 loss to Novara. On 23 June 2011, Grosseto bought out 50% of his rights in a co-ownership deal, for a fee of €300,000. The co-ownership deal was renewed in June 2012. After becoming a regular starter at Grosseto, Crimi was frozen out of the first team along with teammates Yaw Asante, Davis Curiale and Giovanni Formiconi all being in a car involved in an accident where the driver had been drink driving. In June 2013, Grosseto acquired Crimi outright from Bari.
On 3 September 2013, Crimi joined Serie B side Latina on loan. His impressive form in the heart of the midfield, led Latina to an impressive 3rd-place finish in Serie B, after helping beat his former club Bari in two legs in the Serie Bplay-off semi-final, Latina were undone 4–2 on aggregate by Cesena in the two legged final for promotion to Serie A. In June 2014, Latina excised the option to sign Crimi outright.
Crimi joined Bologna on 20 August 2015 for a €730,000 fee, with Daniele Paponi moving in the opposite direction for free. Crimi signed a reported three-year contract, worth €250,000 a year.
On 4 January 2016, Serie A side Carpi had reached an agreement for the loan of Crimi until the end of the season, with a buyout option. On 21 June 2016, Carpi announced that they had activated the buyout clause to sign Crimi on a two-year deal, for a fee of €500,000.
Cesena
On 31 January 2017, Crimi joined Cesena on a temporary deal, with an obligation to buy.
Virtus Entella
On 31 August 2017, Crimi was sold to fellow Serie B club Virtus Entella.
International career
On 4 November 2011, he received his first call-up to Italy U-21 by Ciro Ferrara for the double engagement with Turkey and Hungary qualifier for the UEFA European Under-21 qualifiers. Becoming the first player in the history of Grosseto to play in the Under-21s. On 27 May 2013, he was included as Devis Mangia in the 23-man squad to for European Under-21 Championship in Israel, where Italy finished in second place with Spain beating Italy 4-2 in the final on 18 June, with Crimi making 3 appearances in all the tournament.