The short and simple answer seems to be that we don't know, or at least that Taiping plans for the non-'18 Provinces' part of the Qing empire have not been studied in any great detail. Or at least, that's before I went on a source dive.

There are a couple of instances where we get some vague indication as to the Taiping conception of the geographical space of their hoped-for postwar settlement, but these are rare and, moreover, inconsistent. The issue is that the Taiping never got to the point where the issue of what would happen to the empire became a serious problem to consider. While the revolutionaries of 1911 eventually adopted the 'Five Races Under One Union' idea in an attempt to retain some grasp over the Qing's Inner Asian empire, this adoption seems to have occurred as it was becoming clear that the revolution would succeed and the geopolitical consequences would have to be reckoned with.

Based on the index in Franz Michael and Chung-li Chang's The Taiping Rebellion document collection, I've found five instances in Taiping internal sources that might give some indication as to what the Taiping's intentions with the wider Qing empire were, and various references in Western sources give some further details from which it may be possible to make reasonable speculations.

The first thing to say now is that Tibet, Mongolia and Xinjiang seem not to have been of particular importance on the Taiping radar. The only clear reference to these regions that I'm aware of come in Hong Rengan's 1859 'New Treatise on Aids in Administration' zizheng xinpian 資政新篇, in which he derides several regions for their maintenance of Buddhism and its corruptive influence. Below I've reproduced the version in Chinese on the Chinese Text Project and the English translation in Michael and Chang – evidently, the latter was translated from a different version of the text than the one on the CTP, so text that only comes in the latter version has been put in square brackets.

馬來邦、秘魯邦、澳大利邦、新嘉波、天竺邦、皆信佛教，拜偶像，故其邦多衰弱不振，而名不著焉。不過中國從前不能為東洋之冠冕，暫為失色，良可既已。

Malaya, Peru, Australia, Singapore, India[, Nearer Tibet, Farther Tibet, Mongolia, and Manchuria] all believe in Buddhism and worship idols, hence these countries are as a rule weak and debilitated, and their names are not well known. [The Manchus, although in the past they have robbed and occupied the territory of China and Mongolia, have not dared to claim these territories as their former property; therefore, they have not been regarded highly by other countries.] However, the fact that China in the past has failed to be the leader in the Orient and has temporarily lost its glory is indeed deplorable.

This is not very easy to understand, and probably the translation has an added obfuscatory effect. Inconveniently, the most interesting passages for our purposes are omitted on the Chinese Text Project and Wikisource versions, making it impossible to check the original meaning. Worst-case scenario is some sort of political censorship at work, but optimistically it is quite possibly because the originals are indeed rather incongruous. Alternatively, it may reflect the fact that there are three extant copies of the text and it is possible that there are differences between them, with the online versions drawing on a different one. Regardless, there seems to be some idea that a strong China would exercise a degree of dominion over its neighbours. However, at the same time the suggestion that Tibet, Manchuria and Mongolia were separate entities suggests that the Taiping may not have planned to exercise administrative control over them.

Except.

Elsewhere in the text, Hong Rengan suggests that the Taiping should 'first, in the twenty-one provinces, build twenty-one great roads' (「先於二十一省通二十一條大路」), which implies that a post-war Heavenly Kingdom would encompass not only China's traditional eighteen provinces, but also the three provinces making up Manchuria. Was Hong simply repeating a particular stock phrase (the 21 provinces) without really thinking about it? Or was this a genuine indication that Manchuria would fall under Taiping rule? Given that elsewhere in Taiping materials, there is frequent reference to the idea of eighteen provinces being subject to three, this perhaps should be read as deliberate.

So, what else do we have? 'A Hero's Return to the Truth' qinding yingjue guizhen 欽定英傑歸真, published in 1861, gives some further hints. It takes the form of a dialogue between Hong Rengan and an unnamed interlocutor, who is clearly a Han Chinese official who had deserted the Qing, but not converted to the Taiping cause. At one stage, the official has this to say:

「噫！我中邦大國論人多則有二十倍子韃妖，論地廣則有七倍於滿洲...」

"Alas! Our China is a great country, in population twenty times that of the Tartar devils, and in area seven times that of Manchuria..."

The use here of manzhou 滿洲 for 'Manchuria' is particularly unusual because the term in Chinese use had originally been as an ethnonym, transliterated straight from manju ᠮᠠᠨᠵᡠ, while the region was usually known as manzhouguo 滿洲國, 'Manchu country' (Elliott 2000). The Taiping here were diverging significantly from traditional usage. Anyway, digression aside, the key thing here is the distinction being drawn between zhong bang daguo 中邦大國 ('central great country') and Manchuria, in direct opposition to the Qing redefinition and use of 中國 in a manner that encompassed all the territory held by the Qing state. The problem is trying to assess whose idea this is and where it came from. Is this a position that had always been held by the official himself? Is this an effect of the ongoing dialogue with Hong Rengan (this particular statement comes around halfway through)? Or is this a product of editorial meddling by Hong Rengan, other Taiping censors, or even possibly Hong Xiuquan himself? Whatever the case, its inclusion as part of the unnamed official's epiphany suggests it could be indicative of a Taiping position as to the geographical space of China. There's just one problem. It doesn't clearly suggest whether the Taiping were going to conquer Manchuria anyway. Hong Rengan's brief statement in the 'Royally Approved Veritable Records While Conducting Military Campaigns' qinding junci shilu 欽定軍次實錄 about the Manchus' minority rule and their siphoning of China's wealth is again indicative of his rejection of the Manchu assertion of a 'Great Qing Integrated Domain' daqing yitong 大清一統 synonymous with 'China' zhongguo 中國, but as with the Hero's Return, there is little indication of whether the Taiping would conquer Manchuria nevertheless.

The other problem is that this is very much Hong Rengan's perspective on things. Looking at the one Taiping source that seems to allude to the issue without being written by Hong Rengan, Taiping commander Li Shixian's letter to the British, French and Americans in November 1864, calling on the Western powers to support the (now nearly defeated) rebel cause, briefly says:

...to conquer and subdue an empire of eighteen provinces, combined with a strong army off Mongols and Chinese, who have ample munitions of war and provisions, must be extremely difficult.

The implication here being that for this lesser Taiping commander, their hoped-for conquest may well have terminated at the Great Wall, encompassing only the core 18 provinces of China.

A response to a call by Lin Zexu (the old veteran of the Opium War) for the Taiping to stand down in 1850 was met with a distinctly frosty response, and again the idea of the 'eighteen provinces' oppressed by the Manchus comes up (I haven't included the text here, but it can be found in Lindley's Ti-Ping Tien-Kwoh and Callery and Yvan's L'Insurrection en Chine). As above, the idea of liberation is clear – the question of further expansion is not.

The closest we get to some sort of idea of an early Taiping position in this direction comes from a letter by French missionary Stanislas de Clavelin, dated 6 January 1854 but describing events during the Cassini mission in Nanjing in December 1853. During the Cassini mission, de Clavelin had a conversation with one of the older Taiping converts from Guangxi, and records his interlocutor saying:

“Finally, concerning the Tartars, when we consider the evils that they have caused us, and the abasement to which China has sunk under their government, one cannot dream of entering into an agreement with them; let them return to graze their flocks, or else prepare themselves for a war of extermination. And besides they are idolators, incorrigible idolators. Would the Heavenly Father forgive us for thus forgiving them?"

The implication here is that the Taiping planned to exterminate the Manchus entirely, which would necessitate at least an invasion of Manchuria. However, it still remains the case that the other parts of the Qing empire are not accounted for.

So, with all these materials, what can we conclude? Well, I think it's reasonable to say that, taking all these sundry references together, it's possible to detect a coherent logic and come to a clear understanding of Taiping intentions. In short,

The Taiping didn't have a plan.

Taking the three perspectives we have regarding Manchuria, we have Hong Rengan suggesting that Manchuria would be annexed, Li Shixian suggesting that Manchuria was not part of the Taiping's intended territorial reach, and an anonymous convert in 1853 suggesting that the Manchus would be exterminated, implicitly leaving Manchuria barren. Not unlike the republican revolutionaries in October 1911, the Taiping hadn't reached a stage where they had to really grapple with the problem of what would happen to the broader Manchu empire, having not even secured domination of China. Consequently, the lack of a clearly expressed plan is fully understandable, and the fact that each of our fragmentary sources on this matter points in such different directions is another logical consequence.