The answer depends on your metatheory. In standard feature theory, there is no feature "place" or "manner", so "αplace" or "αplace,βmanner" is meaningless. However, that doesn't stop people from writing rules like that: essentially what they do is redefine the notation and redefine what a feature is (I disapprove, but it happens). The basic problem is that in the linear theory, there isn't anything that refers to classes of features, so you'd have to specifically list all of the changing features, and the rule gets to be pretty big. So this is one of the advantages of autosegmental theory.
This topic actually comes up here, somewhat, in a discussion of what the right formal account of assimilations is. It's clear that we need some mechanism for talking about classes of features, like "place", but there is more than one way to actually get that -- and there is an alternative (first hinted at by McCawley decades ago) to the SPE feature variable notation.
[Clarification] A feature is understood to be a well-defined acoustic state or articulatory action, which either is or is not. Neither "place" nor "voice" satisfy that requirement, so "place" can't be a feature. Ladefoged did propose multi-valued features that would include place, but those were features in name only, since at the time the only concept that was available for representations was "feature".
[On numbers] Use of the numeric transformational format as found in early statements of reduplication is another possibility for total assimilation, if and only if your theory allows such unrestricted rewrite rules. Phonologists generally hate them. The general format for Arabic-like rules would be
1 2 → 2 2
The notation also could be used for partial assimilation, e.g. place only, by adding the non-changing features to the target element, e.g.
[+cons,αvoi,βnasal,γlat...] [+consonantal] [αvoi,βnasal,γlat]
1 2 → 2 2
which means "make the copy of term 2 have the features of voicing, nasality, lateralism... that input term one had"