Would you allow tenants to "overlap"?

[Sam Leon]

Have a somewhat unique situation here.

Tenant got a job transfer out of state.  Gave me 60 days notice.  Moving out end of October.

Great tenant, pays on time, good communication, absolutely no issue.  I am happy for her, even with the lease break I will give her a glowing recommendation.

However, on the business side, I have 4 months left on the lease, and end of October is hard to rent a place, it's practically dead until January.

The lease has a two month early termination penalty.  I would have to charge that, then if I can find another tenant, I will refund everything back to her minus the days I lost rent.

Now, she has a friend of a friend who has visited her and expressed very high interest to rent her place.  She is ready to sign the lease now even if it's almost 2 months away.

I will of course have to go through the process of having her fill out an application, background check etc etc etc...BUT there is a catch.

She needs a place sooner than it's available.  If the current tenant moves out on Oct 31, I need a week to turn it around.  It can't be made available until Nov 7.  She wants to move in second week of October.  That means they will be co-inhabiting the place for 3 weeks...in a one BR unit.

I am not excited about this arrangement.  Sure they know each other, but first, I have no opportunity to really clean out the place;  There will be a period where the current tenant has a lease and the new one is an unofficial "roommate" or vice versa;  If I found a hole in the wall three months in I wouldn't know if it's caused by whom;  I have 4 units with 6 parking spaces, and that would reduce to 5 for a few weeks;  Plus other issues I haven't thought of that some of you may bring up.

Thoughts?  Should I consider it or stick with the dates with no overlaps?