One problem you will face is that some mobile phones are just awful at networking and they can have drastic effects on some networking protocols.
This question comes up a lot in mobile testing and its often confused with testing the backend. Unless your mobile app is specifically peer-to-peer then it seems you want to drive your backend with multiple users.
If the purpose of your test is just ‘can a user login more than once’ then you could just do an exploritory test by driving the API with Postman.
If you want to simulate one user trying to DOS you with multiple logins and check you mitigate , i would take the postman materials and repurpose them into JMeter tests like Dimitri T suggested.
It seems like this is not a high value test in that its about safegaurding your infra which doesn’t have a clear user value because it fundamentally about bad users. Obviously a DOS attack is not great but you can just lock out that user.
Its important to consider the value of the test when deciding how much effort to put in.