I think I did a total of 27 interviews, that was really too many. I'd suggest between 15 and 20 as a more typical and wise number, but the number shouldn't be the main focus. By now you should have some sort of connections with some people at some firms. You should know enough about the firms that they are starting to look different and hopefully a few stand out as a particularly good match for you.
Also, just fyi some schools have screening where firms can more or less chose with whom they wanna interview. I think this prevents firms and students from wasting eachothers time (i.e. there's no point in making a high end firm interview with a low-end student). Some schools don't do this and its a pure lottery. Mine is in the latter group. The very worst student could pref the very most competitive firm first and would almost certainly end up interviewing with them.
All this to say, if your "reach" interviews are of the former type where the firm could have excluded you if they chose, then perhaps they aren't such a reach. If your school takes the latter approach, its possible that the reach firms are huge reaches and you may want to hedge a bit.