I certainly believe that this is possible. Moreover, I think that one should accept the significant support for First Past The Post (FPTP).
The Jenkins proposal of having two votes seems to me to be basically flawed since it then requires a mathematical adjustment to correct the mis-representation from the single member constituencies. Why not have just one vote, which either elects your chosen candidate for the single-member constituency or is transferred to the 'county' vote?
With an additional 20% to be elected at the 'county' level, and STV being the electoral mechanism, one needs about 15 single member constituencies to be merged into counties. These counties would therefore elect three members, giving useful voter-choice and good proportionality.
What would such a scheme look like from the point of view of the voter? The single-member voting would retain FPTP and hence would correspond to the existing system apart from a 20% increase in the size of these constituencies.
This implies that votes which would undeniably be 'wasted' under the present system would now be transferred to the county vote. Here the voter has a bigger choice, but more difficult decisions to make. With perhaps 12-20 candidates to rank in order to elect 3 people, the situation would be very similar to that of the voter in the Irish Republic. The key difference is that this STV vote would only apply to those voters who did not select a winning candidate at the single- member constituency level. Surely this scheme would end the need for strategic voting. The use of the Alternative Vote, as proposed by Jenkins, would therefore be unnecessary.
If voter choice is to mean anything at all, surely the voter must be able to choose between candidates of the same party. By having STV with three seats, such a choice would be effective. Increasing the size of the STV areas would have some advantages in terms of proportionality, but would probably give a ballot paper that was too cumbersome (compared with current practice).