These days, I read documents related with M8 system messages , tolerances , invoice reduction etc.
In this document , i work on implementation and configuration SAP MM Logistic Invoice Verification. My example contains a example which it prevents different postings based on quantity and amount. We will get a problem that i want to post bigger amount, sap will not give permission with error messages finally invoice reduction will solve our this problem.
You can get details : MM-IV-LIV-CRE Set Tolerances for Incoming Invoice - ERP SCM - SCN Wiki
Related Oss notes&KBA :
1372102 - IMG documentation: Set Tolerance Limits
786810 - MM IV: Tolerance check when you enter invoices
313190 - MR1M: Tolerance groups not taken into account
963185 - MM IV: Tolerance check for entering and releasing invoices
791036 - Tolerance check on account assignment item
608041 - Tolerance checks with service-related invoice verification
1598731 - No payment block if the lower limit is exceeded during invoice posting - MM-IV
2054815 - MR8M: Not able to cancel a credit memo due to tolerance limit error.
134976 - Tolerances for blanket purchase order
396095 - MRBR: Message M8215 for tolerance key 'DW'
610340 - No tolerance check for the credit memo
1880413 - Duplicate Invoice Check functionality does not work
158611 - MR1M: Block of invoices for services
753286 - Moving average price becomes very low
90013 - Tolerance limits not converted to local currency
1890543 - Cannot set message "M8 082" as an error at company code level
1853807 - MIR4: Message M8 084 as error message stops posting
1919689 - MIRO: User tolerances are not taken into account
I have a PO , my person posted a material document 100 qty.
In Miro , can you post more quantities and amounts ? Is it related your tolerances ? Not at all.
If posting exceed your tolerances , you can post but it is blocked. If not, you can not prevent. Sometimes , you can not be aware of tolerances when you can post fastly. It is dangerous.
Examples :
1 - Amount is bigger than PO.
2- Quantity and amount are bigger than migo and po values.
What can i do ?
Firstly , check your LIV system messages.
You can update your M8 / 81-82-83 messages with ERROR also if you get them.
MM/Logistic Invoice Verification/Invoice Block/Set tolerance limits
* Please check DQ and PP tolerance keys.
However , it is not enough to prevent posting . You have to maintain your LIV system messages.
* I configure M8 messages with ERROR.
* When i post our invoices , sap will not give permission...
** Unfortunately , i have to post some like a weigher result , vendor errors invoices with variances , how can i solve this problem ?
**Sometimes , you can post your invoices with tolerance even though you implement system messages. Invoice reduction can help you.
*Select layout : Invoice reduction , Correction ID : 2 Vendor error - reduce invoice ,Invoice amount Acc to Vendor , however you can use similiar way for quantities. Sap will create one more fi record for differences.
Results :
** Configurations :
You have to configure your T030 table with RKA transaction (OBYC tcode) and invoice document types.
I add RK document type for invoice reduction. (OMR4)
However, if you want to update some datas to implement in your country like a tax rates ..
You have to update records with enhancement implementation program LMRMCF07 .
I hope that it can be benefical for your business life thoughts.
Thanks a lot for spending times ... 
Regards.
M.Ozgur Unal