1.Talk to Bluffnix in Lower Jeuno. 
Bluffnix will ask you for:
   Dhalmel Leather, 
   Dhalmel Hide, 
   Steal Ingot, 
   Peridot. 
After you give him all he want, he will make your bag limit up to 35.(5 extra than before) 

2.Talk to Bluffnix in Lower Jeuno after you finish Goblin Bag Quest 1. 
Bluffnix will ask you for 
   Ram Leather, 
   Linen Cloth, 
   Mythril Ingot, 
   Turquoise. 
After you give him all he want, he will make your bag limit up to 40.(5 extra than last time) 

3.Talk to Bluffnix in Lower Jeuno after you finish Goblin Bag Quest 2. 
Bluffnix will ask you for 
   Tiger Leather, 
   Velvet Cloth, 
   Gold Ingot, 
   Painite. 
After you give him all he want, he will make your bag limit up to 45.(5 extra than last time) 

4.Talk to Bluffnix in Lower Jeuno after you finish Goblin Bag Quest 3. 
Bluffnix will ask you for 
   Cermet Chunk, 
   Silk Cloth, 
   Darksteal Ingot,
   Goshenite. 
After you give him all he want, he will make your bag limit up to 50.(5 extra than last time) 

I am not sure if you need fame to make this quest pop up. 
If your fame is not high enough, just do more those simple quests in 3 countires,
because the fame in Jeuno is the sum of the fame in 3 countires.