C1 English Grammar Profile point 62 in the category of FUTURE is defined as:
present simple after speech act verbs expressing suggestions and obligation.
l cannot recommend that you go heliskiing.
But remember where we left off because I insist you finish later.
This is not easily located formally in corpora but we can start with a search in iWeb for the speech act verbs in the EGP examples and shift to the right those that do not show a present verb:
suggest|recommend|insist * * * *
5 RECOMMEND THAT YOU DO NOT 1978
10 RECOMMEND THAT YOU USE THE 1218
11 RECOMMEND THAT YOU USE A 1160
18 SUGGEST THAT THERE IS A 801
20 SUGGEST YOU TAKE A LOOK
I suggest you take a look in the mirror, pal.
To take a look into the mirror or looking into the mirror it means to see yourself bare and flawed. No one is perfect, no one is without sin, so to look in the mirror and see all that you are, means to know the person within. (nygal.com)
22 RECOMMEND THAT YOU TAKE A 672
27 RECOMMEND THAT YOU CHECK OUT 637
30 SUGGEST YOU DO THE SAME 631
32 RECOMMEND THAT YOU READ THE 625
33 RECOMMEND YOU TAKE A LOOK 587
*There were no examples of ‘insist’ in the top one hundred.
2 INSIST THAT THERE IS NO 130
8 INSIST THAT THEY ARE NOT 47
9 INSIST ON THE FACT THAT 44
11 INSIST THAT IT IS A 44
12 INSIST THAT IT IS THE 42
13 INSIST THAT THERE IS A 42
15 INSIST THAT IT IS NOT 37
16 INSIST THAT THEY DO NOT 36
17 INSIST THAT THEY DO N’T 35
18 INSIST THAT THIS IS THE 35
*The following example doesn’t contain present simple directly after the speech act verb.
Chinese, Female, level 4, writing
I strongly recommend finding a conversation partner if you want to make your foreign language just like your native language!