You can have a separate document that you supply, alongside the BOM, which matches internal part numbers in the bom to a range of acceptable component part numbers. Then you only have 1 document to update if you want to add/change a new alt part.
Afaik altium has no internal feature for this. So you'd have to create something in excel or something.
This is exactly what we do currently, we have a Access database which contains one table with internal part numbers and another with MPNs, we can then map the two together with a form and our alternative parts list. I'm probably doing a shit job of explaining myself as this is definitely not uncommon, every company who deals with a decent number or PCBAs that I've dealt with uses internal part numbers on their BOMs.
https://www.siliconexpert.com/acl/The reason we can't update BOMs is because of our change control process as we produce medical products, our alternative parts process allows us to add a new part to our alternative parts list (providing it has the same parameters) with much less hassle. This is especially important the last year or so, without doing it like this we'd be redoing BOMs every build.
We want to use Managed Components in Altium (Pro or Enterprise) as we want to get the benefit of the other features such as built in where used reports, supply chain information, revision control, custom workflows such as part creation and requests etc. The managed components feature gets us halfway there, you have a design ID and then use part choices to add specific MPNs. It just seems to be a missing feature not being able to export the complete list.
An example of a segment of our APL:
DesignID Manufacturer MPN
CPN01 Texas Instruments INA180A2IDBVR
CPN01 Texas Instruments INA180A2IDBVT
CPN02 Texas Instruments INA181A3IDBVR
CPN02 Texas Instruments INA181A3IDBVT
CPN03 Texas Instruments HD3SS214IZXHR
CPN03 Texas Instruments HD3SS214ZXHR
CPN04 Texas Instruments CDCDB800RSLR
CPN04 Texas Instruments CDCDB800RSLT
CPN05 Texas Instruments TUSB8020BIPHP
CPN05 Texas Instruments TUSB8020BIPHPR
CPN05 Texas Instruments TUSB8020BPHP
CPN05 Texas Instruments TUSB8020BPHPR