Movement of data from one data file to another within PRIMARY Filegroup
There's no direct command for this.

You can cause enough data movements using ALTER TABLE or ALTER INDEX with the REBUILD option table by table or index by index, so that the new storage allocated by the rebuild will come from the new files. I.e., this will cause "emptiness" of the mdf file for each rebuild. And then finally a shrink (not using EMPTYFILE, but to the desired size, same size as the other files) will do whatever movements there is left to do (the pages allocated to the part of the mdf file that will be removed).

Note though that this final shrink will fragment your indexes and if you care about index fragmentation you would be in for another rebuild.

The reason for using rebuild first is for you to control the pace, doing bits by bits. And also because the shrink code can be horribly slow (for instance if you have heaps and LOBs).