How to separate a column based on words made up only of upper case in R

I want to separate a column of string characters. In one column I want all capitilized words. The strings can have one or two uppercase words. Here is an example of the dataframe:

mydataframe <- data.frame(species= c("ACTINIDIACEAE Actinidia arguta", 
           "ANACARDIACEAE Attilaea abalak E.Martínez & Ramos", 
           "LEGUMINOSAE CAESALPINIOIDEAE Biancaea decapetala (Roth) O.Deg."),
           trait= c(1,2,4))

I tried with separate and the following regular expression: "\\s+(?=[A-Z]+)". This is not working. For the strings with more than two capitilized words it separates the first and the second capitilized words, removing the rest of the string. Here is the code:

mydataframe <- mydataframe %>%
              separate(species, into = c("family", "sp"), sep ="\\s+(?=[A-Z]+)")

This is the result of the code:

I want the following format:

I think we can use (base) strcapture for this to find the last occurrence of two upper-case in a row, then blank space, then a word with at least one lower-case letter.

mydataframe %>%
  mutate(strcapture("(.*[A-Z]{2,})\\s+(\\S*[a-z].*)", species, list(family="", sp="")))
#                                                          species trait                       family                                 sp
# 1                                 ACTINIDIACEAE Actinidia arguta     1                ACTINIDIACEAE                   Actinidia arguta
# 2               ANACARDIACEAE Attilaea abalak E.Martínez & Ramos     2                ANACARDIACEAE Attilaea abalak E.Martínez & Ramos
# 3 LEGUMINOSAE CAESALPINIOIDEAE Biancaea decapetala (Roth) O.Deg.     4 LEGUMINOSAE CAESALPINIOIDEAE  Biancaea decapetala (Roth) O.Deg.