Update to MySQL 5.7 and high disk space consumption
ibdata1 never shrinks.
.ibd files never shrink.
When a table is in ibdata1 and is ALTERed, space in that file is temporarily consumed, thereby possible stretching the file.
With .ibd, an ALTER will probably create a new copy, then toss the old one, thereby temporarily using diskspace, then releasing it.
There are too many variables to make any predictions.  But a fairly safe rule is to never fill up more than half the disk.


The best thing going forward is rather painful:


Dump all the tables
Toss ibdata1 (or make a fresh install)
Turn on innodb_file_per_table
Reload the dump file.


That will 


leave a small ibdata1 file, which is necessary for meta data, etc.
Create each table in its own .ibd file.
Allow future ALTERs to only temporarily consume extra disk space.


Another thing to note:  innodb_file_per_table (ON or OFF) applies only to tables CREATEd or ALTERed after that.  All existing tables say either in ibdata1 or .ibd until such an action is taken.  Correlary:  It is possible to have some tables in ibdata1 and some in separate .ibd files.  It may be beneficial to put small tables in ibdata1 (OFF) and large ones in .ibd files (ON).