You can make parted list the partition table in units of sectors,
then ensure that (assuming 512-byte sectors) each partition's
start sector is divisible by some round number, like 2048
if you want them to be 1MiB-aligned.
For example, here all partitions are MiB-aligned, except
for the first one, which is only 32KiB-aligned. But since it's
only for grub, that is ok:
$ parted -m -s -- /dev/sdb u s p free
Please do not use parted's "move" command. It is risky since it tries
to be smart and is file-system aware. In addition to moving the partition
it may try to move an embedded file system, too, but its built-in FS-aware
code is so old and unreliable that it is slated to be removed altogether.
If you try to use that sub-command (or e.g., mkpartfs which is in the same
boat), recent versions of parted will emit a big warning telling you some
of the above.