Ami probably wouldn't meet a new girl with "You want to be friends"?  
She's shy, remember?  If she's Akane's twin, then presumably she's 
defined her identity as the Anti-Akane and vice versa.  Where Akane is 
physical and extroverted, Ami is intellectual and introverted.  Of 
course deep down they'd probably have some fundamental similarities, 
such as both being prudes and Akane would be smarter than she let on, 
while Ami would have a well-concealed temper.

Of course it's hard to imagine Ami and Akane being twins without Akane 
having some Silver Millenium identity.  One interesting thing is that 
Ami is now 16, the whole run of Sailor Moon would already be behind her,
and Usagi and the other Inner Senshi would likely be attending Furinkan.

You'd need a new major villain, and probably a fair chunk of the 
standard Ranma cast would fall under it's sway, including the Kunos and 
Ranma.