Thank you. I believe I have resolved my problem. I have purchased Office 365 Personal.

1) On my desktop, which runs single-install 2013, 2007 and 2003, when I tried to install 365, I got a warning that 2013 had to be uninstalled. Cancelled that install temporarily.
2) On laptop 1 (W10), which runs 2007 (32 bit) and 2003, I installed 365 (32-bit) successfully. All three versions run independently.
3) On laptop 2 (W7), which runs 2007 and 2003, I installed 365 (32 bit) successfully.
If no problems come up, I will uninstall 2013 on my desktop and install 365 there as well.
At $69 a year for 5 systems, I am satisfied with this solution.
Thanks for your reply and help.