The same speculations made for fertile NNJ can be done for NNTr, for example Silver Bells, which is fertile and I think in many cases forms NTr-Pollen and egg cells. Equivalent crosses as with NNJ can be made.The result of Silver Bells (NNTr plus one chromosome) crossed with NJ-pollen from NNJ should be NNTrJ. Spring Chimes and Quick Bells may have the same constitution,but their parents are Silver Bells and Quickstep(NNJJ). Cross a diploid species with a tetraploid standard daffodil or a tetraploid species like N. viridiflorus and you get some fertile plants, which you can use for the described crosses and many others.
I know, that Peter Brandham writes in his article ‘Triploidy in Narcissus, the Fertility Debate’ (Daffodils 2002-2003): ‘…the probability that allotriploids will produce viable haploid or diploid gametes falls practically to zero’. But Silver Bells (NNTr plus one chromosome) crossed with N. triandrus concolor (TrTr) has Ice Chimes as descendant with 22 Chromosomes, which can only be NTrTr plus one chromsome. Two further descendants from Silver Bells OP are Lapwing and Mission Bells. With 29 chromosomes they are NNTrTr plus 1, which surely comes from self pollination of an NTr egg cell with an NTr pollen. For the effect of NJ pollen there are no examples in DaffSeek. But in any daffodil to be generated it should be possible to proof by measuring the nuclear DNA content, that NJ pollen and other NX pollen are produced and effective for some NNJ or other NNX (allotriploids) in a higher rate.
In autumn 2007 and 2008 I saw many N. x alleniae in Southern Spain. The pollen of some plants looked good, observed with the naked eye. The chromosome constitution is VVM, in which M stays for one chromosome set of N. miniatus. N.miniatus is originally composed of two chromosome sets of N. serotinus and two sets of N. elegans, an autumn flowering Tazetta. The chromosome set of N. elegans consists of 20 chromosomes, which divide into two groups of 10 during meiosis. To be seen are four groups of 5 chromosomes. This special situation may support some fertility. I found two plants each with ten sprouting pollen under the microscope. If the pollen is VM there are many interesting possibilities for crosses. Standard daffodils with red or pink crowns may be a partner. The descendants can be plants with red in the corona, some flowers per stem, flowering perhaps in autumn. Crosses with NNJJ and Silver Bells are further possibilities. They should have more flowers per stem than the foregoing group and be of good vitality and attractive form.
The combination of standard daffodils (NNNN) with N. dubius (JJJJPP) leads to NNJJP. P means a chromosome set of N. papyraceus. Because the plants posess only one P; they are in most cases not fertile.But the situation is not too bad, because the two sets of N and J have no problems to divide by reduction division during the process of meiosis. I found this year one seedling of Ufo x dubius, which showed ten sprouting pollen under the microscope. In 2007 I saw one sprouting pollen from (Patriarch x Rockall) x N. dubius. In most cases the pollen should be NJ or NJP. Crosses with tetraploid sorts like Pink Step, with Matador or Poeticus Daffodils and with N. triandrus can have interesting results.
I think most of the descendants of the proposed crosses should be hard enough for our winters, some especially the autumn flowering types may grow better in a more Mediterranean climate.
I would be delighted, if other hybridizers would find more fertile daffodils under their new seedlings or listed daffodils, which were thought to be infertile till now. Further progress in daffodil breeding should be the consequence.