I'd only pick up and knit down if it's a top-down sweater. If you knit it bottom-up, try this.
*Dream Swatch in Madil Eden Bamboo
On the needles:
*Isabella from Spring Knitty
*Striped hoodie from Nursery Knits
*Tomato from Knitting Daily
I'm hunterjenn on Ravelry. Come find me!
It can be done. (Recently did similar to pocket linings.) Unseam both sides and snip a stitch in about 1" from one side and few rows up from bottom...or depending if rib, etc where it'll work best. Slowly unravel/unpick the stitches in the snipped row and prepare to put those sts on ndl. (If need be, run ndl or extra yarn thru row above where you'll be undoing.) Make sure you have the same no of sts as you orig worked. Knit to whatever length you desire and BO. If front/back worked separately, make sure you you add same no of rows.
If uncertain, work up swatch with scrap yarn and test the process on this beforehand. Doing it this way elim the need for any grafting which some find tricky.
Sara's blog 'Let me explaiKnit' has a description of how to lengthen sweaters, I think near the start/first few months' worth of posts on the blog. The gist is that it is best done in stockinette, unravelling to a destination row (see the videos here and Google explanations of this term). Let us know if you have difficulty finding resources, we're happy to help further then.