Yes, both effects can apply to the same spell.
There's nothing in the wording of either feature to indicate that it excludes other features adding damage as well. Many other combinations of features can work this way -- a barbarian's damage bonus from Rage is cumulative with their Strength damage bonus and other bonuses such as the Dueling fighting style. The word all of these have in common is add.
Contrast this with Thirsting Blade, which says:
You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.
It doesn't say "you can attack one additional time", so the reason it doesn't stack with Extra Attacks is that neither one adds attacks, they both just change the number of attacks from one to two.
This is also similar to how the barbarian and monk Unarmored Defense features don't "stack" with armor. Armor provides one way of calculating AC, Unarmored Defense provides another. A given character can only use one.
So, in general, effects or features that let you add something to a roll are cumulative, but effects or features that change a value are not.
Maximum damage is 428
Here's how (I added some things to make the damage more consistent; average is 418.791):
The Cast
Your Character (let's call him Cody from now on) is a level 20 Goblin (ASs: 10/13/12/18/16/13) with these classes...
- Wizard 10 ---------- [for Empowered Evocation and 2 ASI]
- Cleric/Druid 1 ----- [for Cleric/Druid spell list]
- Sorcerer 4 ----------[for 1 ASI, Extended Spell, and Wild Magic Surge]
- Warlock 1 ---------- [for Hexblade's Curse]
- Bard 2 -------------- [for Jack of all Trades]
- Fighter 2 ----------- [for Action Surge]
... who gets expeditious retreat and shield from his font of magic and carries these items:
- Spellbook containing magic missile and bestow curse
- 6 Spell Scrolls containing contagion (may not need all of them)
- Ioun Stone of Insight (attuned)
- Ioun Stone of Intellect (attuned)
- a wealth of Spell Scrolls containing shapechange
Your Target (let's call her Tessa from now on) is a gas spore because of their exceptionally low Constitution and Wisdom. (although any creature that is not immune to disease or resistant/immune to force, cold, or necrotic is valid if they fail the saves)
The Process
- Cody prepares the spells magic missile and bestow curse after a long rest.
- Cody casts shapechange from a scroll with Extended Spell (trying again if he fails the check, 50% chance; attuning to a Luck Blade and/or acquiring the Lucky feat from a special trainer increase the save significantly). This will allow him to transform into a one-eyed shiver (PoTA 207) for the Chilling Mist trait.
If the one-eyed shiver deals damage to a creature in this area, the creature also takes 5 (1d10) cold damage.
- Cody casts expeditious retreat and shield for 2 hours until he rolls 33 or 34 on the Wild Surge Table (restarting from step 2 and resting as necessary).
33-34 Maximize the damage of the next damaging spell you cast within the next minute.
- Cody uses a contagion spell scroll (trying again if he fails the check, one from Action Surge; +7 vs 15 yields a probability over rounds 2-7 is 1 - 35%^7 = 99.94%) to cast Contagion (Flesh Rot) on Tessa; she will fail every save.
Flesh Rot: The creature's flesh decays. The creature has disadvantage on Charisma checks and vulnerability to all damage.
- Cody casts bestow curse (5th level) on Tessa selecting the fourth option; she will fail the save.
While the target is cursed, your attacks and spells deal an extra 1d8 necrotic damage to the target.
- Cody places Hexblade's Curse on Tessa.
You gain a bonus to damage rolls against the cursed target. The bonus equals your proficiency bonus.
- Cody waits for Tessa's flesh to rot.
- Cody casts magic missile with a 9th level slot selecting Tessa as the target for every missile. Tessa takes extra damage from Fury of the Small.
When you damage a creature with an attack or a spell and the creature's size is larger than yours, you can cause the attack or spell to deal extra damage to the creature. The extra damage equals your level.
- Tessa explodes and 2d4 baby Tessa float slowly toward Cody making him question his decision.
The Calculation
f is force, n is necrotic, c is cold
- Each missile has base damage of 1d4 + 1 force
- Each missile deals 6 extra force damage from Hexblade's Curse
- Each missile deals 5 extra force damage from Empowered Evocation
- There are 11 missiles
- The spell deals 20 extra force damage from Fury of the Small
- The spell deals 1d8 extra necrotic from bestow curse
- [11*(1d4+12) + 20 f + 1d8 n]
- Tessa is vulnerable to all damage 99.94% of the time from contagion
- [1.999*(11*(1d4+12) + 20 f + 1d8 n)]
- The damage is maximized from Wild Magic Surge
- [1.999*(11*(4+12) + 20 f + 8 n)]
- The creature then takes 1d10 cold from Chilling Mist
- [1.999*(11*(4+12) + 20 f + 8 n + 1d10 c)]
This makes 391.804 force, 15.992 necrotic, and 10.995 cold damage for a total of 418.791 damage on average [Max: 428]
Best Answer
I don't think this has been answered simply.
Jeremy Crawford has said the following about the Magic Missile spell:
The specific rule this is taken from is (PHB p.196):
And the Magic Missile spell (PHB p.257) states that the missiles strike more than one target at the same time:
Thus the process is:
Thus any spell damage bonus from an ability such as Empowered Evocation (PHB p.177) applies once to the damage roll, but that damage roll is applied for each missile.