PrestaShop XML Importer is conciliable with the multishop.
For this, it is only necessary to specify the shop or the shops in the flows.
Addition of a product in the shops 1 and 3:
<products>
<product external-reference="demo-3">
<shop>1</shop>
<shop>3</shop>
<reference>ref01</reference>
<name>Name</name>
<description>Product description</description>
<price>19.99</price>
</product>
</products>
Beware, if the external reference is not specified, the product will be created twice (once by shop).
Addition of a product in the shops 1 and 2. then the modification of the title is needed in the shop 1:
<products>
<product external-reference="demo-4">
<shop>1</shop>
<shop>2</shop>
<name lang="en">Name</name>
<description lang="en">Product description</description>
<price>19.99</price>
</product>
<product external-reference="demo-4">
<shop>2</shop>
<reference>ref01</reference>
<name lang="en">New name</name>
</product>
</products>