The "traditional" handling of Exodus 20:3-4 (in the numbering of the standard English translations) -- that the current v. 4 is its own clause/sentence, distinct from v. 3 -- ought to be followed for reasons of both syntax (the ways in which words are ordered to form sentences) and semantics (the meanings of the words).
In this list of commandments, there is a very regular pattern of mostly negative commands (lōʾ + verb) mixed with a couple positive ones (vv. 8 and 12). There are some "off-line" comments as well, but this is the "spine" of the list:
20:3) lōʾ yihyeh lĕkā... [do not have...]
4) lōʾ taʿăśeh... [do not make...]
5) lōʾ tištaḥĕweh... [do not worship...]
7) lōʾ tiśśeh... [do not take...]
8) zākôr... [remember...]
10b) lōʾ taʿăśeh... [do not do...]
12) kabbēd... [honour...]
13) lōʾ tirṣāḥ [do not murder]
14) lōʾ tinʾāp [do not commit adultery]
15) lōʾ tignōb [do not steal]
16) lōʾ taʿăneh... [do not bear false witness...]
17) lōʾ taḥmōd... [do not covet...]
Clearly, then, the pattern suggests that v. 4 begins a new clause, there being no connection, conjunction, etc., which would "bind" it to the preceding.
On the other hand, the remainder of v. 4 does have such a conjunction. Furthermore, it would be very odd in this regular setting to have a "fragment" as an independent ... "bit" which, if it was separated from its context, might be translated this way:
4b) wĕkol tĕmûnâ ʾăšer baššāmayim mimmaʿal [and any likeness which is in the heaven above]
wĕʾăšer bāʾāreṣ mittaḥat [or which is on the earth below]
wĕʾăšer bammayim mittaḥat lāʾāreṣ [or which is in the water under the earth]
And, frankly, that just doesn't make much sense as a distinct clause in this context. For good reason has this been taken as an elaboration of the preceding pesel "idol, image" at the end of the first clause of v. 4.
All words have a range of meaning. Their "lexical" value -- in a dictionary, the description of that range -- is something abstract. In any given utterance, context constrains the meaning, and if there is ambiguity ("I'm going to the bank") it helps to know if we're dealing with a financier or a fisherman.
In Exodus 20:3-4, the context is "worship", so the various terms ("gods", "idol", "forms", etc.) even if they can bear other meanings in other contexts (or might slightly elude us because of the remoteness of the language) still participate in this network of meanings, much as any of the many English translations attempt to convey.
As ever, when thinking through a text, the better question to ask oneself is "What does this mean?" -- and the superficially similar question, "What can this mean?" is best resisted.