Completely agree with you Dr. Mona. That is my working definition anyway....

I do use the term basosquamous carcinoma but never without qualification and a comment on biological behavior. These are my categories.
1. BCC (basosquamous with malignant squamous component): has areas of typical BCC (BerEP4 strong, EMA always negative in the BCC-like component) that transitions merges / blends intimately with the malignant squamous component. Our threshold for this diagnosis is high ~1% of all BCC we report i.e. the malignant squamous component has to be high grade and totally indistinguishable from a high grade SQC in a reasonable area of the tumour (e.g. a whole low power field x5).
2. Basaloid SQC: can simulate BCC very closely and we even published a case with monster cells (mimic of pleomorphic nodular BCC) that did subsequently metastasise (it was quite small too). EMA present in the basaloid epithelium often and BerEP4 can be weak to moderate and relatively widespread. But these tumours lack the hallmarks of bone fide BCC i.e. prominent palisading with mucin in the retraction space.
3. Collision tumours: Have the morphology and IHC of the separate diagnoses SQC and BCC uncommon but have several examples.
4. Basosquamous carcinoma NOS: in the [u][b]rare[/b][/u] cases that I cannot place it in to categories 1. to 3. or into another diagnosis like high grade adenosquamous carcinoma (porocarcinoma high grade) etc. I think this is actually very uncommon and I explain that it needs to be managed as a high grade SQC.
I lump keratotic (central keratinisation in islands so not usually a problem with distinguishing from 1.) and infundibulocystic/TE-like BCC with nodular BCC (the latter can be exceedingly difficult to distinguish from TE especially on the central face. In my experience by very wary about reporting a TE-like lesions in a superficial biopsy from the central face on the sun-damaged, pale, skin of 50+ age group, 19 out of 20 will be TE-like BCCs and can have trapped reactive Merkel cells in this location although we do find CD10 useful - if in any doubt advise conservative complete excision).
Lastly I would not trust any paper on "metastatic BCC / basosquamous BCC" that did not confirm the diagnosis with IHC (and I am not aware of any such paper other than case reports). Many cases of so-called metastatic basosquamous (BCC) are probably basaloid SQC that are simply mimicking BCC.

Forgot to say I usually disregard superficial metatypical / atypical squamous component (in BCC) just deep to ulceration which is very common indeed. Normally the deeper aspect of the underlying BCC is one of the usually types.

Thank u so much Dr Carr for this detailed comment :-)