How do I merge categories for crosstab in pandas where some categories are common?

A while ago I asked this question

But that does not cover the case where two merged categories might have a common category

In that case I wanted to merge the categories A and B into AB. What if I have categories A, B, C and I want to merge A,B into AB, and B,C into BC?

Suppose I have the data:

+---+---+
| X | Y |
+---+---+
| A | D |
| B | D |
| B | E |
| B | D |
| A | E |
| C | D |
| C | E |
| B | E |
+---+---+

I want the cross-tab to look like:

+--------+---+---+
|  X/Y   | D | E |
+--------+---+---+
| A or B | 3 | 3 |
| B or C | 3 | 2 |
| C      | 1 | 1 |
+--------+---+---+

I think you can use crosstab by all unique values and then sum values by selecting by categories in index values:

df = pd.crosstab(df.X, df.Y)
df.loc['A or B'] = df.loc[['A','B']].sum()
df.loc['B or C'] = df.loc[['C','B']].sum()
df = df.drop(['A','B'])
print (df)
Y       D  E
X           
C       1  1
A or B  3  3
B or C  3  3

EDIT: If want general solution it is not easy, because is necessary repeat groups with rename like:

df1 = df[df['X'] == 'B'].assign(X = 'B or C')
df2 = df[df['X'] == 'C']
df = pd.concat([df, df1], ignore_index=True)
df['X'] = df['X'].replace({'A':'A or B', 'B': 'A or B', 'C': 'B or C'})
df = pd.concat([df, df2], ignore_index=True)

df = pd.crosstab(df.X, df.Y)
print (df)
Y       D  E
X           
A or B  3  3
B or C  3  3
C       1  1