I believe Cattleya walkeriana (a species) is a seasonal bloomer, not sure if that will flower more than once a year.
My favorite cattleya alliance that bloomed on every new growth was Rby. (formerly Blc.) Golden Tang. As it matured, this plant bloomed all the time and was deliciously fragrant.
My understanding is that there are very few species that bloom 2x or more per year. So if you really want blooms more than once per year, you are more likely to succeed with a hybrid, particularly a mini catt (as others have noted -- that is also assuming that you are giving it the conditions it wants)
Here are a couple that bloom for me several times a year.
C Bob Betts X C Maxima (very fragrant)
BLC Copper Queen
BL Yellow Bird
Bc Maikai
Brassavola Nodosa
Potinara Krull’s Mini-Buttercup (Pot. Matt Saftenberg x Pot. Jack Crawford)
Stlma Kelly 'Lea'
Mine all grow outside and get a lot of bright sunlight. Stlma Kelly 'Lea' is my best bloomer followed by C Bob Betts X C Maxima.