If you are doing some work which is VAT-exempt and some work which is Vatable then you should be reclaiming a portion of the VAT on your purchases using some sort of apportionment (usually this is based on ratio of VATable sales to VAT-exempt sales but any ratio is fine so long as you can justify it)
VATable here means that the work would normally have VAT charged on it if the client had no 13B exemption
It is irrelevant whether your customer has a VAT13B or not, if the work done is VATable then you are entitled to claim back a portion of VAT on your purchases
In the case of subcontractors doing work and invoicing you, again if the work done is VATable then they should charge you VAT and you can reclaim it (in this instance I would NOT apportion the VAT). If you then invoice the multi-national you don't charge VAT because they have a 13B. In this scenario you will be entitled to a refund of the VAT charged to you by your subcontractor.
For example
SD engages DB to provide consultancy to Multi. DB charges SD €1,000+€230 (VAT) and then SD charges Multi €1,200 (No VAT because Multi has a 13B exemption)
SD can reclaim the VAT of €230 charged by DB as the work done is VATable. There is no VAT to pay as there is no VAT charged by SD to the Multi due to the 13B exemption
Incidentally is it still called 13B - I think it might be a Sect56 exemption now or something like that