Hello BiggerPockets!

I'm fairly new to the BP community and very new to real estate investing. I purchased a duplex in December of '18 and moved in my first tenant this past February. I've learned a lot throughout the whole process of searching, purchasing, and renting, and plan to continue the growth of knowledge and experience. That said...

My tenant, a single mother of three energetic little ones, is asking to move in her friend, a soon-to-be single mother of two. She claims the stay will be temporary, but I know that "temporary" is relative. The Unit is 1350 sq. ft., has 3 bedrooms and 1 bathroom, and has shared laundry. I'm aware of the local code (Chicago) regarding occupancy limits, and am not concerned about exceeding that limit with seven people living in the Unit. I'm considering accepting the new tenant, but want to make sure all my bases are covered. 

My suggested amendments to the current Lease are as follows:

1.  Increase rent $100 per month for utilities surcharge.

2.  Charge a non-refundable move-in fee for the new tenant if she plans on moving in large furniture.

3.  The current Lease allows for pets under 35 lbs, however, the current tenant does not own a pet. For the amendment, I plan to not allow any pets. I think five little kids will be enough.

4.  Add a provision requiring that should one tenant move out, the other will have to pay the full rental amount.

Of course, I plan on running a full background and credit check on the new tenant, as well as make sure she has enough income to cover the rent in full should my current tenant decide to move out. Is there anything I'm missing? Should I not consider accepting the new tenant?

Thanks for your comments in advance!