I think you can try to impersonate that user at the time that re-calculateing discount like this:

//Before re-calculating discount

var user = _userManager.FindByEmail([customer's username]);
if (user != null)
{
    var adminUserName = User.Identity.GetUserName();
    _signInManager.SignIn(user, false, false);

    //Do re-calculate discount here

    //Back to customer service's user
        var adminUser = _userManager.FindByEmail(adminUsername);
        if (adminUser != null)
            _signInManager.SignIn(adminUser, false, false);
}

This sample code is referenced in Quicksilver B2B project https://github.com/episerver/QuicksilverB2B/blob/master/Sources/EPiServer.Reference.Commerce.Site/Features/Users/Controllers/UsersPageController.cs

Hello Binh and thanks for the info! 

I ended up doing it like this for our project, but your solution helped much on the way!

var currentPrinciapl = PrincipalInfo.CurrentPrincipal;
var coupons = order.GetFirstForm().CouponCodes.ToArray();
try
{					
	IPrincipal cartUser = PrincipalInfo.AnonymousPrincipal;             
	var customer = _customerFacade.Service.GetContactById(order.CustomerId);
	if (customer != null)
	{
		var user = Membership.GetUser(customer.Email);
		var _userImpersonation = ServiceLocator.Current.GetInstance<IUserImpersonation>();
		cartUser = _userImpersonation.CreatePrincipal(user.UserName);
	}                
	PrincipalInfo.CurrentPrincipal = cartUser;                
	foreach (var coupon in coupons)
	{
		AddCouponCode(order, coupon);
	}
	order.ApplyDiscounts(_promotionEngine.Service, new PromotionEngineSettings());
}
catch (Exception e)
{
	_log.Error($"Failed to calcualte discounts for order {order.OrderLink.OrderGroupId}. Message: {e.Message}");
}
PrincipalInfo.CurrentPrincipal = currentPrinciapl;