Is there a limit to the number of holes bored in a joist?

You need to provide more information before your question can be properly answered.

Yes, the location of the holes are code compliant.

But that is only 1 aspect of a code compliant joist.

As you know, meeting the limits on one section of code does not exempt you from the others.

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Can you please provide:

The requirements for a joist used in the intended location. (Specific use center 1st floor or roof on a 3 story house is just 1 example that location of use could change the answer.)

The type of wood, and information about any treatments that is being used in the joist in enough detail to be able to determine its load bearing properties under the code that applies to lumber strength. (Oak vs Pine as an example)

The calculations used to determine that the holes in the joist do not have a negative effect on its strength. (Not only deadweight loading, but things like empty holes allowing for more rapid spreading of fire, will be critical)

I am sure there are other variables, but as only the IRC applies, these items are critical, and will hopefully allow you to be given an answer with a high degree of confidence.

Thanks

If there is nothing in the code of practice which specifies a limit to the number of holes, then there is no limit to the number of holes.

From an engineering standpoint, this is because a beam with holes in it can act like a truss (see e.g. the bailey truss). The minimum hole sizes and minimum spacing is to allow enough timber to act as the vertical/inclined "truss elements". Therefore if it is ok to have two large, closely spaced holes at any arbitrary position along the beam, then it is ok to have holes of that diameter and spacing the whole way along the beam.

Structural engineer here. This answer is late, but better late than never.

Notches (cut-aways from the edge) have more requirements due to the flexural (bending) nature of beams: the upper and lowest most fibers of the wood member take the most stress and control the design strength of a beam. See the figure linked below for specific requirements, taken from the IRC.

While the hole locations are less strictly controlled in the IRC, you want to avoid them in the outer ~1/4 of the joist span, as that is where the maximum shear occurs which is designed using the bulk of the wood material, not just the top and bottom fibers like in flexure. I don't think this is codified anywhere, but it's a good rule of thumb.

In summary: Holes should be limited to D/3 in the middle (1/2) of the span and I would limit holes to 1" or D/8, whichever is smaller (this is not codified, but is reasonable), for the outer (1/4) of the span. Holes should never be outside the middle (1/3) of a member. Weyerhaeuser recommends 2x[Hole Diameter] minimum clear distance between holes for their TJI products, which would be a conservative rule of thumb to apply moving forward. I also wouldn't drill holes above each another.