Suppose I call a plumber over to fix my sink, and I say, "Hey, I've also started building a guest house out back--I'd like the interior plumbing run and the whole building connected to the city water. Can you get started on that, too?"
The plumber could say:
A) Let me schedule a time to come back and look at that and give you an estimate.
B) We just do repairs, not new construction. [Let me give you the card of my friend who does that kind of work.]
C) We're completely booked for new construction right now. I don't expect to have availability for that sort of thing until September.
What no plumber will ever say, though, is (D) "Uh, sure...I'll get started on that as soon as I finish this sink, and I guess the $150 for the sink should pretty much cover that."
If you said (D), what you are doing is simply a terrible idea that will not serve you or your client well. But you don't have to keep doing it! You just need to have a conversation where you say, "I gave you an estimate for X. We are now doing YZA. I apologize for not having this conversation earlier--when we switched from X to Y, or when we added Z. But now that we've also added A, I realize belatedly that we need to restructure this project."
Apologize politely and sincerely but not excessively for your actual mistakes--you didn't manage the project and client expectations well. Don't apologize for doing your job well, or for insisting--even belatedly--on the project conditions necessary to do your job well.
If you haven't said something ridiculous like (D), and your compensation and timeline (and compensation timeline) have adjusted appropriately with the project scope, then...well, you may have just bitten off more than you can chew on this project.
That's ok. It happens. Same kind of conversation: "This project has become too big for me to manage while moonlighting. <polite apologies> Can we break the project into phases, or can I help you find someone able to complete a project of this size in a timely fashion?" The client may be disappointed. They may be angry. But the longer you try to be superman and just somehow get it all done because it HAS to be done, the worse the situation gets for you and them. And odds are the client will actually value clear communication and plausible plan-making, even belatedly.