Supplementary European search 
As a rule, a supplementary European search must be performed for each international application entering the European phase and a search fee must be paid. For an exception see point 583 ff. Like any European search report, the supplementary European search report is accompanied by an opinion under Rule 62 EPC, the European search opinion (ESOP), on whether the application and the invention to which it relates meet the requirements of the EPC. As a further service, the information sheet "Information on Search Strategy" is annexed to all supplementary European search reports as from 1 January 2018 (see point 230). The supplementary European search report together with the search opinion is known as the "extended (supplementary) European search report" (EESR).
No search opinion under Rule 62 EPC will be issued if the applicant:
has filed the request for examination according to Rule 159(1)(f) EPC and
has waived the right to be asked under Rule 70(2) EPC whether he wishes to proceed further with the application (see points 600 and 603)
before the supplementary European search report has been transmitted to him. Instead, a communication will be issued under Rule 71(1) or 71(3) EPC, respectively inviting the applicant to correct and/or amend the application or informing him of the text in which the EPO intends to grant the patent. If the applicant requests reasoned amendments or corrections to the text intended for grant, the examining division will issue a further communication under Rule 71(3) EPC if it gives its consent to the amendments or corrections provided by the applicant. Upon fulfilment of certain conditions applicants are given the option to waive the right to receive this further communication under Rule 71(3) EPC.
The supplementary European search is performed on the basis of the last set of (amended) claims available to the EPO on expiry of the time limit set in the Rule 161/162 communication (see points 497 ff). That set of claims is considered the final set at the time the search is performed (see point 488). Any claim for which a claim fee due has not been paid will not be searched (see points 619 ff).
If third-party observations were filed during the international phase and forwarded by the IB to the EPO as designated or elected Office, they will be considered in the supplementary European search report, provided they are substantiated and meet all formal requirements. Furthermore, provided they were not filed anonymously and the third party has explicitly so requested, the EPO will expedite the issuing of the first office action in the (European) examination phase. 
If a supplementary European search is carried out, the European Patent Bulletin will mention the date of despatch of the supplementary European search report. The report is not published, but is available through file inspection. 
If during the supplementary European search the EPO comes to the conclusion that the application contains more than one independent claim in the same category which does not fall under the exceptions listed under Rule 43(2) EPC, it may issue an invitation to indicate, within a time limit of two months, the basis on which the search is to be carried out (Rule 62a(1) EPC). Similarly, if it is impossible to carry out a meaningful search on the basis of all or some of the subject-matter claimed, an invitation to file, again within a time limit of two months, a statement indicating the subject-matter to be searched will be issued. Any declaration of no search, or a partial supplementary European search report issued subsequently due to failure to overcome the deficiency, takes the place of the European search report.

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EPC Articles

EPC Implementing Rules

EPO Guidelines - B Search

EPO Guidelines - C Procedureal Aspects of Substantive Examination

EPO Guidelines - E General Procedural Matters

EPO Guide for Applicants, part II Int.

EPO Guide for Applicants, part II Int. - C The EPO as ISA and SISA

EPO Guide for Applicants, part II Int. - E Euro-PCT procedure before the EPO as designated or elected Office

Offical Journal of the EPO