Cable company Tivo working with your existing tivos depends on the company, I have Mediacom who are beginning to use Tivos as their whole house dvr solution and their's will not play well with standard tivos.
With Mediacom, you can't combine accounts so transfering from one to another will not work and they won't allow you to combine mak 's together. What might work is using the mini to stream off both but I'm not sure. Also, I understand that my cable companies TiVo doesn't allow TiVo desktop so there you can't transfer to and from with your pc, they also don't currently support the Tivo Stream but plan to in the future.
Another issue might be cost, Mediacom TiVo service will cost almost twice what TiVo would charge monthly with of course, you don't have to spend the upfront cost of buying the hardware so that's something you should check with your cable company to inquire their MO they monthly cost. Mediacom is offering their service only to new customers and there is offer for $99 a month fee which includes a 4 tuner Premiere, 2 minis, Internet service and the expanded digital channel lineup. At least with Mediacom, new service package might be a good deal but they don't offer any savings to existing customers.
You will have to check with your cable company to confirm what will or won't work but the general idea is that the cable companies generally lock the Tivos down to encourage higher monthly income to them. Btw - My cable company are using Tivo 4 tuner Premier and minis for their service, not the newest tivo model but still impressive.
TiVo 3Tb Roamio basic