Hosting one Multi-product site and several single-product sites using one Shopify installation

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I would like to have a single shopify installation but I would like to transparently host 4 themes with these URLs

Multi category web site with many products, up-sale and cross-sale) (has template1)

Single product web site with only one product with all multi category page reference removed, even pressing on logo should not take you to the multi product site above - or it can optionally link to it) (this one is to be displayed in the evening)

and (this one is to be displayed in the morning)

and additonal single product web site (displayed all the time)

This way I could independently have 3 different landing pages and I can have some branding for single product web sites.
Multi-product web site should optionally never point to, but if desired it can, but it will load completely different single product theme in which case pressing on Logo
can take you back to multi-product web site. On the other side if one directly comes to a single-product web site I can optionally allow pressing on the logo to
open multi-product site