"With the option to renew."

Probably 99% of residential leases are for a year term or month to month. (but in the latter case there's nothing to take over - they'd just end their lease). So you're not going to find some lease with multiple years on it to take over, no one has one. Long-term leases can be a thing in commercial real estate (say, a storefront), but pretty much aren't in residential.

You asked about "finding leases to take over". The word for that is a sublet. Someone has an existing lease and is subleasing it to you - a sublet. That is the term you should be putting into your searches if that's what you want.

Now, coming back to the original point. It's possible you can skip the broker fee if you pick up a sublet and then renew the lease when it's up. The landlord doesn't need to list the place, no broker involved.

Some sublet postings will mention that there's an option to renew or the like. You should look for a sublet that says that, and make sure you confirm that it'll be an available option with the landlord before signing.

Considering Boston's typical 9/1 lease cycle, the most likely time to accomplish this would be October-March or so. Pick up a sublet from someone trying to leave with most of a year left on it and renew after.

Units going up for sublet in summer with only a couple months left are usually going to have already been leased to someone else for 9/1. Although occasionally you might find someone who made the mistake of renewing and is now looking to leave. Then you might be able to sign for 16 months or something.

A lot of students who graduate in May look for someone to sublet for the summer, with the option to renew in Sept. plus anyone else looking to get out if their lease will have a renew option.