It sounds like your network logic is incorrect. Assuming you have normal finish-to-start predecessors, that means the predecessor task must finish before the successor task can start. However, you indicate that some of the successor tasks have already started which effectively cancels whatever predecessors that task had.
I suggest you re-evaluate your network logic to better reflect what your plan is doing. If a follow-on task (successor) can start before the previous task (predecessor) is finished you need to determine how the two tasks are related. If the successor task can start independently of a predecessor task's completion, then perhaps there is no dependency and the two tasks should not be linked. Or, another possibility is that the successor task can start after the predecessor task is 75% complete. In that case you can use a start-to-start relationship with a lag, such as shown in this example. Note however, that once progress is declared on the successor task, that modified relationship is nullified.
Another approach is to break the successor task into two parts, the first is independent of the predecessor but the second has a normal finish-to-start relationship like this:
There may be other approaches that better meet your needs but keep in mind that in order to have a dynamic network, every task must have a successor, even if it's just the final milestone, and all tasks should have a predecessor unless that task starts when the project starts. A few start-no-earlier-than constraints may be appropriate but they should be avoided as much as possible.
Hope this helps.
John