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Let's say I have three Thunderfire Cannons, with three accompanying Tech Marines. Now, if I join a 4th Tech Marine, the majority toughness becomes 4-4 at T4, 3 at T7.

But what if I join a Tech Marine on a bike to them? Then I have 3 T4 guys, 3 T7, and 1 T5. Is the majority Toughness still 7?

From the main rulebook in the multiple toughness values section -

"If two or more toughness values are tied for majority, use the highest of these tied values."

If you join another model to the thunderfire cannons, definitely have him on a bike or something to change the toughness so that you can still use the toughness of the cannon itself.

 doctortom wrote:
From the main rulebook in the multiple toughness values section -

"If two or more toughness values are tied for majority, use the highest of these tied values."

If you join another model to the thunderfire cannons, definitely have him on a bike or something to change the toughness so that you can still use the toughness of the cannon itself.

So I thought, but I wanted to double check. Thanks!

It's artillery though isn't it?

From 'Shooting At Artillery' (pg. 64, main rulebook):

If shooting at an Artillery unit, the Toughness of the guns is always used whilst at least one gun remains.

You could have as many independant characters attached to the thunderfire cannon, it would always count as toughness 7 since it is artillery.