It's always tough on the remainder when the first team is picked. But perhaps the first 11 cannot do their job without the second team. For example lift up נָשָׂא uses letters from the first 11, but life חָיָה and salvation יְשׁוּעָה require help from the deeper gutturals, chet ח and ayin ע.
What are these remaining letters? And how do they divide? There is a nice page on the morphology of Hebrew verbs here. The first clues as to how the first 11 letters behave when they are not doing their grammatical work is in these two definitions that are perplexing to the student on first reading Hebrew verb paradigm charts.
Roots that contain a ו vav or a י yod as the 2nd letters are called hollow roots.
Roots that contain at least one of the weak letters, י yod, נ nun, ח ħet, ע ʻáyin, א álef, and ה hey, are called weak roots.These six letters contain the four 'vowels' or 'reading helpers' matres lectiones all of which are in the first 11, and four of the gutturals with only ר resh missing.
What's left? ג gimel, ד dalet, ז zayin, ט tet, ס samech, צ tsade, פ peh, ק qoph, and ש sin (already implicit with shin - though I suppose we could give team 2 an extra player). [Note that ט tet sometimes does replace ת taf after metathesis in the hithpael of verbs whose first letter is the sibilant צ tsade. This is the only case I have found of a true secondment of a letter from team 2 to team 1.]
What can we tell about this second team and how it interacts with the first? Is there a sample set of code where we can observe the workings on the playing field? Perhaps Zephaniah 3:8 would be a good grammatical test... So first 11 are the letters that play a role in grammatical forms (G) and the consonant-only (C) team are the letters that do not. Where a G letter is acting as Consonant only, I will designate it as X, a G in C's clothing.
לָכֵן - GGG a preposition
חַכּוּ־לִי - CXG-GG a weak consonant and 4 grammatical letters with one acting as consonant
נְאֻם - GXX
יְהוָה - XXXX (Proper name)
לְיֹום - GXXX
קוּמִי - CXXG
לְעַד - GCC finally a word that uses more than one non-grammatical letter
כִּי - GG a preposition
מִשְׁפָּטִי - GXCCG
לֶאֱסֹף - GXCX
גֹּויִם - CXXG
לְקָבְצִי - GCXCG
מַמְלָכֹות - GXXXGG
לִשְׁפֹּךְ - GXCX
עֲלֵיהֶם - CGGGG - while ayin is not on the grammatical team, it is almost playing grammar here with its role in the preposition.
זַעְמִי - CCXG
כֹּל - GG
חֲרֹון - CCXX
אַפִּי - XCG
כִּי - GG
בְּאֵשׁ - GXX
קִנְאָתִי - CXXXG
תֵּאָכֵל - GXXX
כָּל־ - GG
So for this verse that uses all the letters of the alef-bet we have 38 letters playing grammatical roles, 20 from the consonantal-only set, and 36 grammatical letters acting as consonants including 4 at my count that are matres lectiones. 40 percent (roughly) of the 94 letters in this verse are acting as grammatical clues and 79% of the letters used are those of the 'first 11', the set of letters that are used in prefixes and suffixes. I may have mistyped a G X or C but hopefully not.
A quick experiment on my poetry corpus shows that 75% of the letters in some 20,000 words are in the grammatical group!