The answer is: Maybe.
Under the 3.5 ruleset this is not an option but some DMs allow in their games all the 3.0e material that has never been revised.
If this is the case, a 3e supplement (Arms and Equipment Guide IIRC) states that any item that gives armor bonuses can be enchanted as if it was an armor.
This includes the infamous Bracers of Armor and the similar object Harness of Armor that does the same but is worn on the body slot (Harness of Armor is detailed in Lost Empires of Faerun).
That's not a shirt but I guess you had nothing important in the "armor" slot anyways.
If you're looking for a tunic (torso slot), the Vest of the Archmagi, detailed in Magic Item compendium should give you the armor bonus you need for further enhancing it. This item has an almost Epic price so it's not viable for further enchanting until character level 21.
If you're just looking for another way to get fortification, there's an enhancedd Ring of Protection in Waterdeep, City of Splendors that could solve your problem as well. (But no silent moves ring, unfortunately)
For getting +1 to +5 enhancements on a nonmagical shirt (or on your vest of resistance), magic vestment does the trick. Ask your party wizard or cleric for some.