Extract common data out of multiple files

I am trying to extract common list of Organisms from different files
For example I took 3 files and showed expected result. In real I have more than 1000 files. I am aware about the useful use of awk and grep but unaware in depth so need guidance regarding it.

I want to use awk/ grep/ cut/ perl/ python to get the needful result.
File A:

Pseudomonas stutzeri A1501
Pseudomonas fragi A22
Pseudomonas fluorescens A506
Aeromonas caviae Ae398
Rickettsiella grylli
Aeromonas veronii AMC34

File B:

Rickettsiella grylli
Pseudomonas fulva 12-X
Pseudomonas extremaustralis 14-3 substr. 14-3b
Aeromonas caviae Ae398
Gallaecimonas xiamenensis 3-C-1
Pseudomonas stutzeri A1501

File C:

Pseudomonas extremaustralis
Pseudomonas fulva 12-X
Pseudomonas extremaustralis 14-3 substr. 14-3b
Aeromonas caviae Ae398
Rickettsiella grylli
Pseudomonas stutzeri A1501

Expected Result file : Common organism

Aeromonas caviae Ae398
Pseudomonas stutzeri A1501
Rickettsiella grylli

Hoping for your suggestions and support.
Thank you in advance