[Anker]

I think I got it.

You have a pinched brake line that barely lets fluid pass. When you initially press the pedal the brake lines that aren't pinched activate the brakes they go to. When you keep applying pressure you slowly push brake fluid through the pinched line.

Here's what I suggest you try.

Try pumping the brakes with each push including the part where your pedal just keeps moving towards the floor. If the second or third push doesn't allow the pedal to go beyond the initial movement I believe my theory has been validated.

If you indeed have a pinched line you can locate which one is pinched by removing the brake pads on each wheel in turn and see if its easy to push the pistons into the calipers. The brake that has the pinched line will be difficult to push the pistons into the calipers.

Hope I am right.