My experiences on both sides of the screen are that anything more than cosmetic adjustments - especially to abilities that players can access - are fraught with weird interactions and unintended consequences; that it's better to build a new thing that either stands next to or replaces the thing that would be tweaked. And, counterintuitively, large-scale changes are less messy than tweaks.
Want your magic missiles to look like fireworks? No sweat.
Want to play a cleric with the druid spell list (and pretend to be a druid generally, but with channels instead of an animal companion)? Almost certainly not a problem: while potent, not a lot of edge cases to worry about.
Want an item that deals "hellfire" damage, which is like fire damage except that it bypasses resistance/invulnerability to fire damage (except when it doesn't, because of reasons)? Just about every combat with fire-themed creatures is a debate. Oh, and does it affect creatures with vulnerability to fire like it's fire? Better just to call it "hellfire" but have it do, say, force (or even raw, untyped) damage and pre-empt all the questions.
And, that's before 5e's philosophy of "just because it exists in the world doesn't mean PCs can do it". 5e intentionally places some abilities out of the reach of PCs (mostly by making them monster abilities). That is to say that 5e goes out of its way to give the GM the permission - and even encouragement - to look beyond the PHB when designing the world.
With that in mind, I would encourage a frame-change: instead of looking at how to tweak Teleportation Circles to fit the story you want to tell, create a new thing that's Teleportation Circle-adjacent.
As an example, this GM would crib something from a 15+-year TV/movie franchise that produced a variant of d20 Modern: the Stargate, though with a better name in your game world; just "gates"?).
A crash-course in Stargates as presented in the series:
- matter can only travel one-way: from the side that opened the gate to the destination
- radio waves can travel both ways (they can use bog-standard walkie-talkies to talk to base)
- gates can be temporarily removed them from the network by being buried
- gates need a nearby "Dial-Home Device" ("DHD") to dial the gate (so, you might get somewhere only to find that you can't gate home)
- without a DHD, dialing is possibly but extremely difficult - both physically and because it requires a staggering amount of energy
- a gate being active means other gates can't dial into it and it can't dial out
- there's a "hard" limit on how long a gate can stay open (38 minutes), but there are a number of effects that extend that for plot reasons
- each gate has a unique address
Those basic rules allow for a fantastic amount of versatility in how important the gate network is in any given story - from "it's how we got to the interesting part" to "it is the interesting part". Further: disruptions in the gate network don't necessarily prevent Teleportation Circle (or other teleportation effects) from working - or vice-versa.
And, a gate network doesn't negate the usefulness of Teleportation Circles generally (eg., wizards might still want them in their towers so they can get home faster; guilds may still have a few for members, etc.).
... and, surely there's no magic out there that can connect to a gate without already having a gate, right? ...