Can you pay an alternative cost like emerge and also pay additional costs on the same spell?

When you cast a spell, you first determine its total cost before paying. The total cost can include an alternative cost plus any number of additional costs. CR 601.2f states that the total cost is calculated by starting with the chosen cost (which may be an alternative cost), then applying cost increases and additional costs on top of it.

Emerge is an alternative cost that lets you pay a reduced generic amount by sacrificing a creature (CR 702.116a). Nothing about Emerge or the rules prevents you from also paying additional costs — such as those granted by cards like Goblin Electromancer effects, or mandatory additional costs on the spell itself, or costs added by opponents' spells/abilities — at the same time.

It is important to note that you generally cannot stack two alternative costs together (CR 601.2b — if multiple alternative costs apply, you choose at most one). But additional costs are a separate category and always stack freely with whichever cost you chose to pay.

Concrete example: You cast Elder Deep-Fiend (Emerge cost: 8 minus the CMC of sacrificed creature) while your opponent has a Thalia, Guardian of Thraben in play, which adds 1 colorless to noncreature spells. You sacrifice a 4-CMC creature, making the Emerge cost 4 colorless. Thalia's mandatory additional cost then increases it by 1, so you pay 5 colorless total. Both costs apply simultaneously at payment (CR 601.2h).

So the rule of thumb: one alternative cost at a time, but layer on as many additional costs as apply.