The NIV translates it as "take many";
the ESV as "acquire";
this online Hebrew Interlinear translates the Hebrew word ("irbe" -- other interlinears say "yarbeh") as "increase": See Online Interlinear
And yes, rabah can also = multiply.
Horses can multiply into generations of horses; wives don't multiply into generations of wives for the same husband (that's called incest).
The reason for not multiplying wives is not a prohibition on polygamy. The reason is to prevent from being led astray.
Think of this word picture -- a fence with a gate.
If, let's say, you had such a fence around your yard as a boy -- and a wild forest on the other side -- sure...the ultimate reason that your father might tell you NOT to go thru that gate is because of where you can wind up -- lost!
Even if we were to agree that the prohibition in such a situation is not that your father had a "thing" about going thru gates; the thing is that that particular gate was a given pathway to "astrayness" -- "lostness" -- then, yes, the given gate does become key.
Elsewise, Deut. 17:17 loses all meaning...Deut 17:17 zeroes in a just a few things that can lead your heart astray: Hoarding wives and hoarding wealth.
It does not prevent the taking of a couple or even several wives. BTW, the proper translation is not many, it is multiply...
The bottom line of Deut. 17:17a is not to take MANY wives. Now I've got "news" for you...by definition, poly = MANY!
The KJV, NKJV, AMP, 21st Century KJV, American Standard, Darby, New American Standard, and Young’s Literal Translation all translate it as multiply.
Your analogy of a fence and a gate is a bad analogy. The correct form would be your father telling you not to go very far into the woods because you will get lost. There is no problem going up to the tree line. You can even go a short distance into the woods, but the further you go, the greater the chances of the consequences of getting lost will occur. There is no prohibition on marrying one wife or two or three. The prohibition is against “a lot”.
In fact, the Common English version translates it as “numerous” and the Contemporary English version translates it to “a lot”.
Further, even if taken literally, and even if the assumption is that multiply means more than one, the law applies to the King. No other person is stated as being bound by that passage.
So once again, King David, which the Bible said was a man after God’s heart, .... how many wives and concubines did he have?