The CP.3 was a tandem, two-seat fighter. The CP stood for Combattimento Pallavicino (after CAB's progettista capo, Cesare Pallavicino).
The CP.3 was also part of the line springing from the CAB AP.1 (Assalto Pallavicino) and its single-seat fighter derivative, the CP.1. An improved derivative, the AP.1bis, led to CP.3. The AP.1bis, MM.243, was basically an AP.1 with rearward retracting undercarriage (a la the PL.3 racer) and thinner wings.
To confuse matters, the CP.3 was the same as the Ca.304. And, for the record, AP.1s were Ca.301s (as was the CP.1, I believe). The weird part is that the CP.3's Caproni designation number comes before the aircraft from which it was derived, the AP.1bis (Ca.305). Go figure :
The designations are a bit odd. Ca.300 series numbers were assigned to CAB. But Caproni Aereonautica Bergamasca assigned the role/designer acronyms before their Ca. designations were applied. (If I understand Skybolt's explanation properly, designs were assigned role/designer acronyms in the design phase. Once CAB had Caproni's approval to build a prototype, the Ca-300 series designation was applied.)
I note in the Caproni designation list, that Ca.302 and Ca.303 are mysteries. Still further AP.1 derivatives/descendants to be uncovered? BTW, further improvements to the AP.1 line led to the HS12-powered Ca.335 Maestrale developed for Belgium as the SABCA S.47.
Correct, but it doesn't stop here. CAB originaly stand as Cantieri Aeronautici Bergamaschi, and was an indipendent company. During the '29 crisis aftermath, Caproni bought a number of companies and incorporated them in varying degrees in his group. CAB was one of this, and sotta Fraschini and Reggiane other two (actually, Reggiane was never fully owned by Caproni Group). So they folowed a different designation system than Caproni's. When they entered the group, the extsant model were changed. Take this as Boeing calling 717 the MD-95.