How can I iterate a vector once and insert/remove/modify multiple elements along the way?

I want to iterate an array/vector once and modify multiple elements on the way as this is the most optimal solution. I don't want to scan it again and again just because Rust is unhappy about borrows.

I store a list of intervals represented as [start;stop] in a sorted vector and I want to add a new interval. It might be overlapping, so I want to remove all elements that are not needed anymore. I want to do it all in one go. Algorithm can look something like this (I cut some parts):

use std::cmp::{min, max};

#[derive(Debug, PartialEq, Clone, Copy)]
struct Interval {
    start: usize,
    stop: usize,
}

impl Interval {
    fn new(start: usize, stop: usize) -> Interval {
        Interval {
            start: start,
            stop: stop,
        }
    }
    pub fn starts_before_disjoint(&self, other: &Interval) -> bool {
        self.start < other.start && self.stop < other.start
    }
    pub fn starts_before_non_disjoint(&self, other: &Interval) -> bool {
        self.start <= other.start && self.stop >= other.start
    }
    pub fn starts_after(&self, other: &Interval) -> bool {
        self.start > other.start
    }
    pub fn starts_after_disjoint(&self, other: &Interval) -> bool {
        self.start > other.stop
    }
    pub fn starts_after_nondisjoint(&self, other: &Interval) -> bool {
        self.start > other.start && self.start <= other.stop
    }
    pub fn disjoint(&self, other: &Interval) -> bool {
        self.starts_before_disjoint(other)
    }
    pub fn adjacent(&self, other: &Interval) -> bool {
        self.start == other.stop + 1 || self.stop == other.start - 1
    }
    pub fn union(&self, other: &Interval) -> Interval {
        Interval::new(min(self.start, other.start), max(self.stop, other.stop))
    }
    pub fn intersection(&self, other: &Interval) -> Interval {
        Interval::new(max(self.start, other.start), min(self.stop, other.stop))
    }
}

fn main() {
    //making vectors
    let mut vec = vec![
        Interval::new(1, 1),
        Interval::new(2, 3),
        Interval::new(6, 7),
    ];
    let addition = Interval::new(2, 5); // <- this will take over interval @ 2 and will be adjacent to 3, so we have to merge
    let (mut i, len) = (0, vec.len());
    while i < len {
        let r = &mut vec[i];
        if *r == addition {
            return; //nothing to do, just a duplicate
        }
        if addition.adjacent(r) || !addition.disjoint(r) {
            //if they are next to each other or overlapping
            //lets merge
            let mut bigger = addition.union(r);
            *r = bigger;
            //now lets check what else we can merge
            while i < len - 1 {
                i += 1;
                let next = &vec[i + 1];
                if !bigger.adjacent(next) && bigger.disjoint(next) {
                    //nothing to merge
                    break;
                }
                vec.remove(i); //<- FAIL another mutable borrow
                i -= 1; //lets go back
                vec[i] = bigger.union(next); //<- FAIL and yet another borrow
            }
            return;
        }
        if addition.starts_before_disjoint(r) {
            vec.insert(i - 1, addition); // <- FAIL since another refence already borrowed @ let r = &mut vec[i]
        }
        i += 1;
    }
}

It fails in a couple of places because of the borrowing rules. Is there a way to either

1. do it with iterators in one go
2. work around the borrowing

There is borrow splitting available, but I don't see how I can apply it here.