This is an excellent question. Yes, there may be issues with IR35 in these situations but any contract work needs to be looked at on its own merit.
If you have taken on a separate contract with a different company, that’s totally independent from your employer, then that contract will need to be evaluated.
If the nature of the contract is very much like an employment relationship, then it could be caught within IR35. However, it may be possible that you as the contractor do not have access to the same facilities as an employee.
There are various pressure points that might mitigate the risk of IR35, such as not working in the employer’s office or not working set contractual hours for the hirer. However, in the current climate, the majority of workers are doing this, for example, working from 7am and finishing early or using their own desks and equipment for work purposes. Each contract will be unique to the contractor and to the worker. You should ensure that you are aware of the potential risks and must undertake any possible steps to mitigate those risks prior to engaging with the contract. You would greatly benefit from speaking with a tax advisor, such as Prashant or Tim, if you have any questions.