by right , not

supposedly you can only do the job that is specificly detailed in your h1 doc. You need to get a sperate H1 for your second job.
However, this is not strictly followed when the the second job is offered by the same organization with the same HR department. If the HR does not say anything, do not bring it up. It is never your fault.
Many HR would rather re-profile the job description of the second job than apply for a new H1.