There ought to be ways to increase any characteristic. Nearly all careers allow stat increases instead of skills if the player selects the Personal Development table during character generation. If there is a game mechanic, no matter how abstract, to increase stats in chargen and well established real life techniques for increasing those abilities, then it ought to be possible to gain increases during play.
The easiest way to reflect stat increases within the current rules would be to allow a bonus equal to the character's Athletics (characteristic) skill for the related characteristic in skill rolls. That option will work for physical stats, but does not address mental characteristics. It also effectively doubles the Athletics skill rating for traditional Athletics skill uses.
A better solution would be to adapt the existing Training rules to apply to characteristics as well. I would suggest using the characteristic DM of the level desired as the equivalent of the skill level for time requirement for each level. Any stat up to seven can be increased by one after eight weeks and a successful (8+) roll with that characteristic. To reflect the relative difficulty of further improvement, double the characteristic DM can be used as a negative DM for the roll, making it easier to raise very low stats, but more difficult (and much more time consuming) to raise high ones.