(A) The one who is desirous of heaven [substitute ‘heaven’ with any other goal] should sacrifice with the Darśapūrṇamāsa [substitute ‘DPM’ with any other goal].

Now, how to identify such condition? Is it always tantamount to the fact of desiring something? Or could one imagine also something like (many thanks to Bama Srinivasan for suggesting it):

Given condition X, one should perform the sacrifice Y, if he desires the result Z.

At first sight, the answer is that such prescriptions just do not occur. Originative prescriptions (utpattividhi) which enjoin for the first time a given sacrifice have the form seen above (A) and no additional conditions are mentioned. By contrast, presriptions enjoining auxiliary rites state further conditions, but without needing to repeat the general condition of the desire because of which one undertook the principal sacrifice.

Accordingly, Rāmānujācārya in his Tantrarahasya (chapter IV, section 4.2.7) explains that in optional (kāmya) sacrifices, such as the one performed in order to get rain, and in occasional (naimittika) ones, such as the one performed when one begets a son, one has only an occasion (nimitta) for performing them. By contrast, in the case of expiation rites (prāyaścitta), one needs an occasion (i.e., something to expiate, namely a ritual mistake) while there is the general frame of the desire-condition which initiated the main sacrifice within the framework of which the expiation rite occurs.

The situation is further complicated by the case of prohibitions. These have two possible forms:

1. One should not harm any living being
2. One should not sleep with one’s wife during the sacrifice X

No. 1 has the form “One should not do X in all possible cases”, a form which is by definition impossible for prescriptions, which always need to highlight a group of addressees (according to the viśvajinnyāya).
No 2, by contrast, has the form “One should not do X in condition Y”. However, also No. 2 is not identical with a prescription, insofar as it states a condition which is not a desire, since only prescriptions lead to the attainment of a desired result.

Is this a further hint of the dissymmetry between prescriptions and prohibitions?

On conditions and desires, see this post. On the project (with Agata Ciabattoni, Björn Lellmann and Francesco Genco, in the framework of which I am working on Mīmāṃsā deontic logic, see this post and the further ones linked to it. All mistakes in this post remain mine only.
I have studied and translated the relevant chapter of the Tantrarahasya in my 2012 book, which you can buy or find in excerpts on googlebooks. An earlier draft of the same book is also available on Academia (but please get in touch with me if you want to use specific parts, and I will tell you whether something needs to be emended.