Here is my data frame. df
store_1 store_2 store_3 store_4
0 banana banana plum banana
1 orange ta
You can try something like this
import itertools as it
corr = lambda a,b: len(set(a).intersection(set(b)))/len(a)
c = [corr(*x) for x in it.combinations_with_replacement(df.T.values.tolist(),2)]
j = 0
x = []
for i in range(4, 0, -1): # replace 4 with df.shape[-1]
x.append([np.nan]*(4-i) + c[j:j+i])
j+= i
pd.DataFrame(x, columns=df.columns, index=df.columns)
Which yields
store_1 store_2 store_3 store_4
store_1 1.0 0.4 0.4 0.8
store_2 NaN 1.0 0.2 0.4
store_3 NaN NaN 1.0 0.2
store_4 NaN NaN NaN 1.0