Updated Janurary 5, 2018 with the addition of more taxa.
Wikipedia reports
“Haramiyidans have been known since the 1840s, but only from fossilized teeth and a single partial lower jaw. However, several features of the teeth have shown for many years that haramiyidans are among the most basal of mammaliaforms. Megaconus (Middle Jurassic, Zhou et al. 2013, Fig. 1) is a member.”
Wikipedia also reports
“Multituberculata is is an extinct taxon of rodent-like mammals. At least 200 species are known, ranging from mouse-sized to beaver-sized. Multituberculates are usually placed outside either of the two main groups of living mammals—Theria, including placentals and marsupials, and Monotremata—but closer to Theria than to monotremes. The oldest known species in the group is Rugosodon from the Jurassic.”

Figure 1. Megaconus in situ. Original tracing and DGS color tracing which appears to show that both hind limbs and the vernal pelvis have been displaced posteriorly — unless their is a counter plate that preserves skeletal parts that don’t appear to be present here.
Recently added taxa
to the LRT (749 taxa then, 1370 taxa when updated) include the purported haramiyid allothere mammaliaform. Megaconus mammaliaformis (Zhou et al., 2013) the mutituberculates Rugosodon (Yuan et al. 2013) and Kryptobaatar (Kielan-Jaworowska 1970). Unfortunately most of the other known haramiyid allothere mammaliaformes are known from too few traits to test in the LRT. So far as I know, only Kryptobataar (Fig. 8), Rugosodon (Fig. 9) and Megaconus (Fig. 1) are known from complete skeletons. There may be others, but these three are enough to test the nesting. In the LRT they nest together with Rattus (the rat. Fig. 3). Additional taxa nest Haramiyavia with pre-mammal trithelodonts.

Figure 2a. Mammals include rodents. Haramiyidans and multituberculates nest with rodents. This is a cladogram from 2016. Compare to a more focused look at primates + glires in Figure 2b

Figure 2b. Subset of the LRT focusing on Primates + Glires.
By contrast…
Zhou et al. 2013 report: “Here we describe a new fossil from the Middle Jurassic that has a mandibular middle ear, a gradational transition of thoracolumbar vertebrae and primitive ankle features, but highly derived molars with a high crown and multiple roots that are partially fused. The upper molars have longitudinal cusp rows that occlude alternately with those of the lower molars.” The first three traits put Megaconus among the pre-mammal cynodonts. The last three traits are specialiizations. The broader traits employed by the LRT put Megaconus in the rodent clade. Rattus (the rat) and Oryctlagus (the rabbit) were included taxa in both studies. The primitive traits appear to be atavisms (reversals).
So now we have a phylogenetic problem.
Do Megaconus and Rugosodon nest more primitively than monotremes? According to Zhou et al. they do. The Zhou team employed more taxa, more traits and more dental traits — by far.

Figure 3. Megaconus mammaliaformis in situ and reconstructed. Compare to the similar, but smaller Vilevolodon.
Unfortunately,
Megaconus otherwise looks so much like a rodent that it has been given the nickname, ‘the Jurassic squirrel.’ The LRT tests only the relatively easy traits to see, not dental details. In the LRT, shifting Megaconus and Rugosodon to Juramaia adds 37 steps. That’s a big hump to get over. I do not know how many additional steps would be added by shifting Megaconus to Rattus in the Zhou et al. study.

Figure 4. Megaconus mandible showing cynodont-like posterior mandible bones, not tiny mammal-like ear bones. Unfortunately this key trait cannot be confirmed with present photo resolution. Mammals and reptiles call the same bones different names in some cases and some of these are labeled here.
If the Zhou et al. team is correct
then we have a problem. If the Zhou et al. team is not correct, they have a problem. They have identified an angular/ectotympanic where there is none. Rugosodon and Kryptobataar likewise do not have pre-mammal-type posterior jaw bones prior to their evolution into tiny ear bones.

Figure 5. Brown Rat (Rattus norvegicus) skull showing how lower incisors are used to scrape away and sharpen upper incisors The ear bones are located inside the circular ectotympanic posterior to the mandible and below the skull.
How can we reconcile this problem?
- If Megaconus indeed nests with Rattus, then the ankle, posterior jaw and other traits may represent reversals to a more primitive state.
- If Megaconus is indeed primitive, then it anticipates and converges on a long list of traits with Rattus under the LRT, Given that living monotremes have a long list of special traits, it is not unreasonable to accept that Megaconus diid likewise. The only caveat to that hypothesis is that monotreme special traits are not shared with or converge with those of other mammals.
- If Megaconus parts have been misidentified, then (no exceptions) all other traits indicate it is a rodent sister.

Figure 6. Haramiyava dentary showing what a more typical stem mammal dentary and teeth look like. Earlier studies linked this clade to multituberculates, but this dentary was cause to reject that association. Just the appearance of that poster medial groove is enough to indicate the presence of tiny jaw bones that had not transformed into ear bones. From Luo et al. 2015.
Stem mammals have lots of teeth
(Fig. 6) and Megaconus does not have lots of teeth. It has rodent-like teeth and everything else is rodent-like, too. And check out that overbite!

Figure 7. Eomaia skull traced and reconstructed. Eomaia nests between marsupials and placentals. Note the unspecialized skull and dentition. Megaconus has a very specialized dentition.
The skull of
Kryptobataar, (Fig. 6) another purported multituberculate, likewise shows no trace of tiny post-dentary bones, either here or in a Digimorph scan.

Figure 8. The skull of the multituberculate Kryptobataar, which now nests as a rodent in the LRT. B&W image copyright Digimorph.org and used with permission.
The skull of
of Rugosodon (Fig. 9) likewise shows no trace of long, gracile post dentary bones, either here or originally.

Figure 9. The skull of Rugosodon. There are no tiny post dentary bones present here according to the original authors or my own tracings.
References
Kielan-Jaworowska Z 1970. New Upper Cretaceous multituberculate genera from Bayn Dzak, Gobi Desert. In: Kielan-Jaworowska (ed.), Results of the Polish-Mongolian Palaeontological Expeditions, pt. II. Palaeontologica Polonica 21, p.35-49.
Luo Z-X, Gatesy SM, Jenkins FA Jr., Amarai WW and Shubin NH 2015. Mandibular and dental characteristics of Late Triassic mammaliaform Haramiyavia and their ramifications for basal mammal evolution. PNAS 112(41) E71010-E7109. doi: 10.1073/pnas.1519387112
Wible Jr, Rougier GW 2000. Cranial anatomy of Kryptobaatar dashzevegi (Mammalia, Multituberculata), and its bearing on the evolution of mammalian characters. Bulletin of the American Museum of Natural History 247: 1–120. doi:10.1206/0003-0090(2000)2472.0.
Yuan CX, Ji Q, Meng QJ, Tabrum AR and Luo ZX 2013. Earliest evolution of multituberculate mammals revealed by a new Jurassic fossil.. Science 341 (6147): 779–783. doi:10.1126/science.1237970.
Zhou CF, Wu S, Martin T, Luo ZX 2013. A Jurassic mammaliaform and the earliest mammalorian evolutionary adaptations. Nature 500 (7461): 163. doi:10.1038/nature12429.
wiki/Rugosodon
wiki/Megaconus