It will depend upon the terms of the first variation.
If it merely directs the 20% elsewhere, or confirms the devolution of the remainder of the (relevant) residuary interest is unchanged, it should be OK to make a variation over all or part of the remaining 80%. If there is potential for the beneficiary to want to make another variation, the wording used should allow for that possibility.
However, if the first variation purports to create a new will, the position is far less certain.
There are, of course various levels between the above examples and it will be a case of considering the effect of the actual words used.
If there is no immediate change to the IHT position as a result of any variation, it appears HMRC does not want to know about it, unless the variation creates a trust, and so may never be scrutinised. In such cases, it appears HMRC is content(!) that, if the appropriate declarations are included, s.142 IHTA 1984 and s.62(6) TCGA 1992 shall apply to such variations. Any challenge might therefore come from anyone who feels disadvantaged by any such variation (e.g. those entitled to the estate of the original beneficiary following their death). To my mind, a peculiar state of affairs