First off there are a lot of rules on combining/overlapping effects:
The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect--such as the highest bonus--from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.
- Player's Handbook: Chapter 10, Spellcasting; Combining Magical Effects
[...] When two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap [...] Game features include spells, class features, feats, racial traits, monster abilities, and magic items [...]
- Dungeon Master's Guide: Chapter 8, Running The Game; Combining Game Effects (errata)
When two or more effects have the same proper name, only one of them applies while the durations of the effects overlap (a duration is a time span of 1 round or more). The most potent effect--such as the highest bonus--is the one that applies, or the most recent effect applies if the effects are equally potent.
- The Essentials Kit: Chapter 0, Welcome to Dungeons & Dragons; Effects with the Same Name Don't Stack
That all said we also know that things with the same name don't stack regardless of how different the actual effects might be, for example:
- If you cast a spell with different effect options twice on the same creature, do multiple castings of the spell stack?
- If you cast Blindness/Deafness as a 3rd level spell, can you target one creature with both effects?
- Do the Stone Golem's Slow feature and the Slow spell combine?
In all these cases, despite the actual effects being quite different, the name of the effect is the same and so they cannot stack.
How do these rules apply to Wild Magic Surges? In particular there are effects such as:
15-16: For the next minute, you regain 5 hit points at the start of each of your turns.
23-24: Your skin turns a vibrant shade of blue. A remove curse spell can end this effect.
61-62: For the next minute, you must shout when you speak.
71-72: You gain resistance to all damage for the next minute.
Can multiple different surges exist, simultaneously affecting the same creature? Are they considered to be the same class feature or to have the same proper name and thus do not stack?
Can multiple of the same surge (such as 15-16 above) exist, simultaneously affecting the same creature? Would you regain 10 hit points at the start of each of your turns or just 5?
How do Wild Magic Surges stack with each other (if at all)?