There is nothing to stop this unless the debts are secured and the enforcement proceedings are for repossession. Standard bailiff proceedings or action from HMRC would be covered by the IVA. If the situation is very serious your IP can get a court order stopping all legal proceedings while the meeting of creditors is held.
My IVA was based around an HMRC High Court Judgement (bankruptcy). They will not play ball unless all your returns are up to date. They can also be difficult if they've had trouble with you in the past although mine went through eventually. My IP said he couldn't believe how hard they made the process even though he'd proven that they'd get more from the IVA than the bankruptcy. In the end they forced me to lodge £2k with the IP in case they needed to bankrupt me again. Not the easiest thing to do when you've just been made bankrupt! Fortunately I was able to do it and it all went through. My £2k was returned to me on completion which was nice but my IP wasn't certain it would be.