Are these high values or not?
The code allowable is just that, the maximum allowed by code. Some factors that should be considered are how accurate you model is and how close to the design will the field installation be. I see no problem designing up to 99 percent of the allowable providing:
There is a constraint in pipe routing that does not allow you reduce the loading. Sometimes there is insufficient room to for large expansion loops.
Careful consideration has been made for the number of thermal cycles that the piping system will go through. If it is a high cycle system, then you should be very careful as you come close to the allowable thermal stress. In contrast if you are designing for a 2000 full cycles and the reduction factor is 1 for 7000 cycles, then there is less concern.
How close are you to the mechanical properties of the pipe? If you are designing a steam system that operates at 350 degF and the allowable stress given in the code is listed at between -20 and 650 degF before a reduction in allowable is given, there is a slight comfort factor here.
There will be no adverse affect on flange loading.
How accurate are the design temperatures & pressures. Perhaps it is time to discuss this with the person that wrote the specs.
There are other limiting details that may give you comfort or concern as you approach 99% of the allowable
So the bottom line is if every allowable factor of the design is pushed to the limit and there is no practical way to reduce the stress, proceed with extreme caution. In contrast, if there are large margins of safety in other limiting aspects, caution still needs to be exercised. If you are uncomfortable with the stress, and I assume you are because you started the thread, you may consider hiring a consultant with more experience to review your work.