Hi parisienne and welcome to the forum
Of course you can start a business whilst subject to an ongoing IVA, but you will need to declare any earnings to your Supervisor in accordance with the terms of your proposal - and at least once per year. If you are earning more, expect your IVA payments to increase accordingly.
Your business venture must also not draw capital away from your household budget, and thus jeopardise your ability to continue to fund your IVA payments.
Don't forget to register as self-employed with H M Revenue & Customs, and file your tax returns on time. Good luck with the business and the remainder of the IVA.
Regards, Melanie Giles, Insolvency Practitioner for over 20 years.
For further details contact me at
http://melaniegiles.com and view my IVA blog at:
http://melaniegiles.blogs.iva.co.uk