Before giving the exact answer, I’d like to confirm what the business and personal account referred to. If you have an Office 365 for Business account (business account) and a personal Microsoft account (personal account), it is not feasible to login to Skype
for Business with the personal Microsoft account.
If you have two Office 365 accounts, one is used for business purpose and the other is used for personal purpose, and then you can use both the two account in Skype for Business. However, it is not feasible to sign into both the two account at the same time
on one computer using the Skype for Business client. You may use one account in Skype for Business client and the other one in
IM in OWA.
Regards,
Yang
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