If you started in a campaign with the limit as times 2, what level of hermetic breakthrough would you roughly put extending the limit to times 3?
Bob
Pretty dang low. It is an inferior version of a lesser virtue, Elder Runes. Now, because the virtue already exists as a Mystery House virtue, to a house which is still upset about losing control of a house virtue, it could lead to quite a few "exciting" stories.....
Depends on whether you (the troupe / storyguide) want the breakthrough to happen in play or not, and how long you want it to take (in both game and real time).
I'd probably make it a Minor Breakthrough since it doesn't really introduce anything new to Hermetic theory, but rather expands upon it in a relatively minor way.
Yeah, but should have another limit: the limit Art should stand like the upper limit (that means than you still limited), that means - you can use until MTx2 or the Art or Arts Score of the Vis than you are using, but if you have less, you still anchored to the MT Score.
I'm the SG in this and I feel like the limit of x2 was too harsh, but instead of divine fiat saying it's now x3, I wanted to give the players an opportunity to do it themselves (or not if it turns out they are not interested, in which case fiat it is.)
the campaign is in Iceland (old 4th ed source book 5th ed rules) so I was thinking of having the local hedgies have no limit on vis (or ond as they call it) but it be very dangerous, to give research material for integration, but if any one has ideas for lab projects that might break the limit I could suggest that would be great as well.
Bob
If your players aren't interested, why change it?
Nah. With that small a discovery, no need for integration material. Integration's too easy anyway. 
I'm on hiatus from the game for a few months (I'm in a different city from them) and want to get ground work sorted out. I have a few NPC's who it would be good to have the restriction broken for, otherwise some plot line would take ages to come to fruition, I could faff around with other stuff to make up the time but I want the flexibility in-game (if the NPC's are going too quickly I can always justfy why they got delayed).
and if I'm going to change this it really ought to be the PC's in the spotlight,
they probably will think of ways to do it themselves, and I'm not going to force them, but if they are short of ideas, I wanted some to throw into the pot.
Bob
You can split the difference. Give that capability to the NPCs, and have them have written out the magic theory tractatus that explains how to do it. If the players never get that tractatus, they have to do it the hard way.