Sure can:

protected override void ApplicationStarted(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
    {
        MemberService.Saving += MemberService_Saved;
    }

    private void MemberService_Saved(IMemberService sender, SaveEventArgs<IMember> e)
    {
        foreach (IMember member in e.SavedEntities)
        {
            if (member.IsNewEntity()) //This is a newly created member
            {
                //Reset token
                Guid resetToken = Guid.NewGuid();
                string setPasswordUrl = CreatePasswordUrl(resetToken.ToString(), member.Email);
                if (!string.IsNullOrEmpty(setPasswordUrl))
                {
                    EmailNewUser(member.Email, member.Name, setPasswordUrl);
                }

                member.SetValue("resetToken", resetToken.ToString());
                ApplicationContext.Current.Services.MemberService.Save(member, false);
            }
        }
    }

You can ignore the fact that the event is Saving and the method is MemberService_Saved; this is because I've been trying different events but I haven't been renaming the method.

No, there is only one saved entity, and it's the event which is being triggered 3 times with the same object as e each time

yep, looks like it, so definitely sounds like a bug.

I'll update the issue tracker and I'll implement a workaround in the meantime.

Thanks for the help Jeroen!

The post is old and I do not know if they have already fixed this bug. When I need to update member property in the event and do not want to fire the event again, I do so:

ApplicationContext.Current.Services.MemberService.Save (member, raiseEvents: false);

Set the raiseEvents variable to false in the method. Always worked