So that is something that you should discuss with your electrician. You may have a line w/neutral in your box unrelated at this point to the switch leg you are working on. (The bundles of blacks/whites suggests that.) So the question to your electrician is can you re-map the 4-way leg so that the line originates in the box as opposed to at the light. This would involve locating the where the line is connected to the lights and properly terminating that connection so that the line is no longer connected to the lights as it is now.
There are other considerations as well. Will adding pigtail connectors to the box overload it? Is the line/neutral in the box on the same circuit as the 4-way? If not, is there any reason the 4-way shouldn’t be on it? etc, etc, etc.
Definitely speak with an electrician if you’re going to explore.