You can use a FilteredAlignment to insert constant sites and set the constantSiteWeights attribute. Say, your original alignment is called xyz, so the XML produced by BEAUti contains something like

It is easiest to rename this to say xyzOriginal,

then add another data element, just after the closing element of the alignment would be a good spot, that say

Note id=’xyz’ and data=’@xyzOriginal’ should match what you have in the XML.

The constant weights at the end add weights for DNA in order A,C,G,T, so it adds 100 constant sites with all As, 200 with all Cs etc.

In the output to screen, it should report statistics of the xyzOriginal as something like:

 6 taxa
 768 sites
 69 patterns

followed by statistics of the filtered alignment

 Filter -
 6 taxa
 768 sites + 1000 constant sites
 69 patterns

where the total number of constant sites added are reported as well.