The 1/6th rule
IRC allows a notch 1/6th of the depth of a wooden joist (but not within the middle third) on the basis that the joist is sized sufficiently for the stress at midspan, and a 5/6th depth beam in the end thirds is hence sufficient for the lower stress experienced there. Hence a 1/6th depth notch will not affect the design capacity of the joist.
Engineering
In engineering terms it is eminently possible to reinforce a beam such that a deeper notch will not cause the beam to fail. A simple rule applicable in this case is that the maximum stress is proportional to the width of the beam times the depth cubed.
Hence, if you wanted a beam that was 1/2 of the depth of the original beam, then in order to provide the same stress as the original beam would have experienced, you'd need a beam that was 8 times the width!
Looking at your numbers, and trying to minimise the width as much as possible, I would say:
* The IRC rules suggest you're allowed a beam depth of 5/6 of 9.5" = 7.92".
* You want a beam that has a depth of 9.5" - 2.5" = 7"
* Hence your depth is reducing by a factor of 7 / 7.92 = 0.884
* Hence your breadth needs to increase by a factor of 1 / (0.884^3) = 1.45
So attaching a wooden joist to the side which is half as wide as your original beam should be sufficient. Alternatively, by using a steel plate (as you suggested) you would need much less material.
However, there are of course key points that I've missed here. You need to transfer the stress from the original beam into the attachment. 441
You would hence need to design connections to transfer the stress, and over an appropriate length.
The real world
In most jurisdictions it should be possible for engineering calculations to be carried out, proving that the reinforcement/modification is sufficient. Once the change is then approved by the local authority (on the basis of the calculations), work will then be able to go ahead. I would advise you to either contact a local engineer or contact your local building inspector.
Joist width vs IRC width
You mentioned in one of your edits (since superseded I believe) that the joist was wider than the minimum required by IRC. Possibly this is because the joist is wider and/or longer than suitable for the minimum width. I would hence advise against thinking "the joist is wider than the minimum width, therefore I can notch deeper". 441