addtional or subsequent saving throw

[Hilary]

Is there a penalty for additional saving throws taken in the same round?

[MoiMagnus]

No.
The DM is always free to give advantage or disadvantage due to circumstances, I'd heavily discourage a general rules of "subsequent saving throw in the same round have a disadvantage".

[Zhorn]

I'd heavily discourage a general rules of "subsequent saving throw in the same round have a disadvantage".
Likewise.
For those unsure of what repeated saves mean mathematically, for each repeated saving throw made of any DC that is neither impossible or guaranteed the probability of getting at least one failure, P(X≥1), notably increases.

As an example I did the math and posted the results in the current Magic Missile thread (https://forums.giantitp.com/showsinglepost.php?p=24930754&postcount=28), where the repeated DC 10 concentration checks can be brutal compared to the DC set from a single BIG hit.