Do convertible loans have to be integer multiples of a debt security?

Yes. The acquisition of equity or shares cannot be partial, so you can only convert outstanding capital corresponding to a whole multiple of the share value.  

For example, in the case of the Biovilla project, if the investor has loaned 2.200€ to the promoter, the investor can convert 2.000€ of the invested capital into 4 Biovilla shares, at the price of 500€ each. The investor will then become a shareholder of the cooperative, holding 2.000€ of its capital. The remaining 200€ will continue to be considered as outstanding capital, to be repaid according to the payment plan previously stipulated in the, initially signed, loan agreement. 

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