I'm wondering if you can make a second craft, profession, or perform skill a class skill upon multiclassing, so that, for example, you could have both Craft (Alchemy) and Craft (Weapons) as class skills as a result.
Yes, but no need to do that; read below.
- If you take a class that has a class skill that you desire, and you put a rank in it, then you gain the +3 bonus.
- If it is a cross class skill, and you put a rank in it, then you don't get the +3 bonus.
- If you have Craft, Profession, or Perform as a class skill, and almost all classes do, then you also have ALL Craft, Profession, or Perform skills as class skills. It is up to you how many different Craft, Profession, or Perform skills you want.
- Classes that share the same class skills do not keep granting a +3 to that skill - it is a one time bonus.
Reference in the PFSRD:
In addition, each class has a number of favored skills, called class skills. It is easier for your character to become more proficient in these skills, as they represent part of his professional training and constant practice. You gain a +3 bonus on all class skills that you put ranks into. If you have more than one class and both grant you a class skill bonus, these bonuses do not stack.
See the wording under the Craft skill for a little more guidance:
You are skilled in the creation of a specific group of items, such as armor or weapons. Like Knowledge, Perform, and Profession, Craft is actually a number of separate skills. You could have several Craft skills, each with its own ranks. The most common Craft skills are alchemy, armor, baskets, books, bows, calligraphy, carpentry, cloth, clothing, glass, jewelry, leather, locks, paintings, pottery, sculptures, ships, shoes, stonemasonry, traps, and weapons.