I have a couple of dozen Twitter accounts and only have one mobile phone number. I think you can skip this phone number step during sign up process. It's not very obvious, but I think it's possible. You can also skip the annoying onboarding wizard (that makes you try and follow a bunch of people) by just changing the URL to the Twitter homepage. It doesn't force you to complete signup wizard as long as you completed the basic steps such as choosing a username and email address.
One drawback of not adding a phone number is that your account is more likely to get suspended. This can even happen immediately after signing up without having tweeted anything. In that case you can appeal the suspension and explain why you had to create a separate business account and can't add a phone number since it's already linked to your main, personal account. If that account is in good standing, then you can expect your new account to be reactivated within a day or so.
I have a couple of dozen Twitter accounts and only have one mobile phone number. I think you can skip this phone number step during sign up process. It's not very obvious, but I think it's possible. You can also skip the annoying onboarding wizard (that makes you try and follow a bunch of people) by just changing the URL to the Twitter homepage. It doesn't force you to complete signup wizard as long as you completed the basic steps such as choosing a username and email address.
One drawback of not adding a phone number is that your account is more likely to get suspended. This can even happen immediately after signing up without having tweeted anything. In that case you can appeal the suspension and explain why you had to create a separate business account and can't add a phone number since it's already linked to your main, personal account. If that account is in good standing, then you can expect your new account to be reactivated within a day or so.