This is one of Hamburg-South America Line's MONTE-Class vessels from the 1920s; they were all identical, even down to the porthole groupings: MONTE SARMIENTO, MONTEO OLIVIA, MONTE PASCOAL, or MONTE ROSA.
Originally there were 5 of them, MONTE CERVANTES to add which sank 1930 in South America.
And sorry Rich, they were not identical. SARMIENTO 1924, OLIVIA 1925 and CERVANTES 1928 were alike, the 1931 pair PASCOAL and ROSA were different not really in size but the glazing on Promenade Deck in front of the bridge included hatch No.3, which is clearly visible on photos of my collection. I think your photo shows either SARMIENTO or OLIVIA (Hamburg-Süd wouldn´t have provided a post card with sunken CERVANTES in 1937) with identical port holes as you said.
Best wishes, Manfred
P.S. Just found the same photo in a book of my collection (Collection Andreas Guhr) stating: Impessions of a Mediterranean cruise on MONTE OLIVIA!