I have a homebrew idea to try and add more power to the sorcerer. The idea is that when sorcerer casts a spell that causes a target to make a saving throw, they can spend sorcery points to add 1d4 to their spell save DC. I'm not sure how many sorcery points this should cost though and was wondering what other people think.
Likely to require a variable cost, consider using the bane spell as a point of comparison
This is assuming your post is seeking opinions.
The 1st-level spell bane causes creatures that fail the save to subtract 1d4 from attack rolls and saving throws. (PHB, p. 216)
Subtracting a d4 from a saving throw, and adding a d4 to the save DC, are mechanically the same, so this is a fair comparison when the spell targets a single creature.
Depending on the spell, adding to the DC could be significantly more powerful than on others. Being able to apply this effect to, say, fireball would be the equivalent of applying bane to all of the creatures in its area of effect. Such a metamagic would have incredible value.
It is safe to assume, then, that without limiting the number of targets the spell can affect, this would be very strong and would likely require a variable sorcery point cost to balance.
If one were to limit it to single-targets only, it is still getting a replicated psuedo-1st-level spell effect on a target. In this case I draw a comparison to Twinned Spell, which allows replication of a spell as well. Twinned Spell costs 1 point per spell level, and given that some higher level spells, such as hold monster become very powerful with a high DC (seeing as it breaks bounded accuracy) I feel it is suitable to mimic the cost of Twinned Spell.
My recommendation would be to make the metamagic cost a number of sorcery points equal to 1 + the number of targets affected, or, instead change the cost to equal the spell level (akin to Twinned Spell) but require it can only have a single target.
Compare Heightened Spell
When you cast a spell that forces a creature to make a saving throw to resist its Effects, you can spend 3 sorcery points to give one target of the spell disadvantage on its first saving throw made against the spell.
Dis/advantage is generally thought to be comparable to a modifier of +/- 5. The one you're suggesting is on average half that, but applies to multiple targets. I don't think this can be easily balanced to be a fixed point, since your proposed metamagic would make already very powerful crowd control spells like Hypnotic Pattern so much stronger.