...
The network is a separate layer from the witnessing, but if you mean the progression of transactions, or that its actually usable, lets go with that. Each user can change 1 witness and witnessing goes on as usual, it doesnt affect how the DAG looks like at all. Its the majority of witnesses which matters, as long as a majority exists, even if several witnesses are replaced with many many other, and only 6 remain, it all still works.
The other question, but a user replaces all or 2 witnesses with his own, has been answered, those are invalid transactions. An attack on Byteball is possible only if already existing witnesses collude and conspire. As you see, it is a very genius concept, a major major invention by Byteball, so it is hard for simpler minds like CfBs to fully grasp it. But he does like to post pictures, look a few pages back when he tried to compare Byteballs DAG to Ethereum blockchain with pictures,

.
He hasnt even read the whitepaper, is just trolling and spreading FUD, every single one of his posts in this thread has been with intent to FUD.
I haven't dove deep into the technicals of this coin, but from what I understand currently all 12 witnesses are controlled by tonych, so at this point an attack is possible if tonych becomes malicious or if he is coerced into doing something. To me, it's not clear how the transition from one person controlling all 12 witnesses to having them be distributed is likely or possible to occur - it would require active intervention on behalf of (almost) everyone making txs on the network, right? Most people don't care about stuff like this, especially if this doesn't happen early - the more users the higher proportion of them will be casual users who don't care about technical stuff like this.