You probably want ST_Split(). 
If you are working with your previous example, one way to avoid precision 
problems after applying the split might be to use the linear referencing 
funtions to shrink the lines by your preferred tolerance.

In case you haven't already seen it, this illustrates the numerical precision 
difficulty:
https://observablehq.com/@mourner/non-robust-arithmetic-as-art


> On Aug 30, 2019, at 1:51 AM, [email protected] wrote:
> 
> Hi,
> What PostGIS command do I use to  breake linestrings or multilinestrings 
> using  another “breaking” table including linestrings or multilinestrings, 
> without erasing any points or adding anything from the “braking” layer?
> Thanks in advance,
> Paul
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